Bernoulli Bibliography

Complete File


Back to Index


ABASON E.,
[1] Sur les "puissances périodiques" et les polynomes de Bernoulli, Bulletin Timisoara, 2 (1929), 183-187.
J56.II.990;

ABE S., KARAMATSU Y.,
[1] On Fermat's last theorem and the first factor of the class number of the cyclotomic field, TRU Math., 4 (1968), 1-9.
Z186.368; M42#4482; R1970,1A138

ABEL N.,
[1] Solution de quelques problèmes à l'aide d'intégrales définis, Oeuvres compl., 2nd edition, Vol.I, Grondahl, Christiania, 1881, 11-27.
J13.20

ABOU-TAIR I.,
[1] On a certain class of Dirichlet series, Kyungpook Math. J., 30 (1990), no.2, 215-225.
Z719.11055; M92b:11062

ABRAMOWITZ M., STEGUN I.A., (eds.)
[1] Handbook of mathematical functions, National Bureau of Standards, Washington (1964).
Z171.385; M29#4914; R1965,5A40k

ABRAMSON M.,
[1] Permutations related to secant, tangent and Eulerian numbers, Canad. Math. Bull., 22 (1979), no.3, 281-291.
Z437.05002; M81c:05007; R1980,9V506

ADACHI N.,
[1] Generalization of Kummer's criterion for divisibility of class numbers, J. Number Theory, 5 (1973), 253-263.
Z263.12005; M48#11041; R1974,3A267

[2] The Diophantine equation $x^2 \pm ly^2 = z^l$ connected with Fermat's Last Theorem, Tokyo J. Math., 11 (1988), 85-94.
Z653.10016; M89g:11023; R1989,2A87

[3] An observation on the first case of Fermat's last theorem, Tokyo J. Math., 11 (1988), no. 2, 317-321.
Z673.10015; M90a:11035; R1989,10A152

ADAMS J.C.,
[1] On some properties of Bernoulli's numbers, in particular on Clausen's theorem respecting the fractional parts of these numbers, Proc. Camb. Phil. Soc., 2 (1872), 269-270.
J7.132

[2] On the calculation of Bernoulli's numbers up to $B_62$ by means of Staudt's theorem, Report Brit. Ass. Advanc. Sci., 1877 (1878), 8-14.
J10.189

[3] Table of the values of the first sixty-two numbers of Bernoulli, J. Reine Angew. Math., 85 (1878), 269-272.
J10.192

[4] On the calculation of the sums of the reciprocals of the first thousand integers and on the value of Euler's constant to 260 places of decimals, Report Brit. Ass. Advanc. Sci., 1877 (1878), 14-15.
J9.189

[5] Note on the value of Euler's constant, likewise on the values of the Napierian logarithms of 2, 3, 5, 7 and 10, and of modulus of common logarithms, all carried to 260 places of decimals, Proc. Roy. Soc. London, 27 (1878), 88-94.
J10.191

ADAMS J.F.,
[1] On the groups $J(X)$, II, Topology, 3 (1965), 137-171.
Z137.168; M33#6626; R1967,7A358

[2] On the group $J(X)$, IV, Topology, 5 (1966), no. 1, 21-71.
Z145.199; M33#6628; R1967,1A341

ADELBERG A.,
[1] Irreducible factors and p-adic poles of higher order Bernoulli polynomials, C. R. Math. Rep. Acad. Sci. Canada, 14 (1992), no.4, 173-178.
Z771.11014; M93e:11029; R1993,4A267

[2] On the degrees of irreducible factors of higher order Bernoulli polynomials, Acta Arith., 62 (1992), no.4, 329-342.
Z771.11013; M94a:11027; R1993,6A257

[3] A finite difference approach to degenerate Bernoulli and Stirling polynomials, Discrete Math., 140 (1995), 1-21.
Z841.11010; M96i:39001 R1996, 11B256

[4] Congruences of $p$-adic integer order Bernoulli numbers. J. Number Theory, 59 (1996), no.2, 374-388. (Erratum: J. Number Theory 65 (1997), no. 1, 179.)
Z866.11013; M97e:11028

[5] Higher order Bernoulli polynomials and Newton polygons. Applications of Fibonacci Numbers, Vol. 7 (Proceedings, Graz, July 15-19, 1996, G.E. Bergum et al., Eds.), 1-8. Kluwer Academic Publishers, Dordrecht, 1998.
Z990.11930

[6] 2-adic congruences of Nörlund numbers and of Bernoulli numbers of the second kind, J. Number Theory, 73 (1998), no. 1, 47-58.
Z926.11010; M99m:11018

[7] Arithmetic properties of the Nörlund polynomial $B_n^{(x)}$, Discrete Math., 204 (1999), no. 1-3, 5-13.

ADIGA C., BERNDT B.C., BHARGAVA S., WATSON G.N.,
[1] Chapter 16 of Ramanujan's second notebook; Theta-functions and q-series, Mem. Amer. Math. Soc., 53 (1985), No. 315, 1-85.
Z565.33002; M86e:33004; R1985,12V38

ADIGA C., BHARGAVA S.,
[1] A simple proof for finite double series representations for the Bernoulli, Euler and tangent numbers, Internat. J. Math. Ed. Sci. Tech., 14 (1983), 652-654.
Z516.10006

ADLEMAN L.M., HEATH-BROWN D.R.,
[1] The first case of Fermat's last theorem, Invent. Math., 79 (1985), no. 2, 409-416.
Z557.10034; M86h:11022; R1985,8A144

ADLER A., WASHINGTON L.C.,
[1] $p$-adic $L$-functions and higher dimensional magic cubes, J. Number Theory, 52 (1995), no.2, 179-197.
Z849.11093; M96j:11147

ADRIAN P.,
[1] Die Bezeichnungsweise der Bernoullischen Zahlen, Mitt. Verein. Schweiz. Versicherungsmath., 59 (1959), 199-206.
Z89.280; M22#5604; R1960,11A802

AGARWAL G.G.,
[1] Bernoulli monosplines and best quadrature formulas, Ganita, 35 (1984), no. 1-2, 70-80 (1987).
Z638.41010

AGOH T.,
[1] On the Diophantine equation concerning Fermat's last theorem, TRU Math., 13 (1977), no. 1, 1-8.
Z366.10018; M56#11893; R1978,6A170

[2] On the first case of Fermat's last theorem, J. Reine Angew. Math., 314 (1980), 21-28.
Z417.10011; M81b:10008; R1980,8A114

[3] On Fermat's last theorem and the Bernoulli numbers, J. Number Theory, 15 (1982), no. 3, 414-422.
Z504.10008; M84i:10018; R1983,8A115

[4] A note on the Bernoulli numbers and the class number of real quadratic fields, C.R. Math. Rep. Acad. Sci. Canada, 5 (1983), no. 4, 153-158.
Z517.12002; M85j:11143; R1984,2A94

[5] A note on the first case of Fermat's last theorem, C.R. Math. Rep. Acad. Sci. Canada, 6 (1984), no. 6, 337-342.
Z563.10015; M86i:11011; R1985,8A145

[6] On the congruences of Voronoi and Kummer for the Bernoulli numbers, C.R. Math. Rep. Acad. Sci. Canada, 7 (1985), no. 1, 15-20.
Z567.10006; M86f:11019; R1986,1A143

[7] On the criteria of Wieferich and Mirimanoff, C.R. Math. Rep. Acad. Sci. Canada, 8 (1986), no. 1, 49-52.
Z585.10009; M87c:11025; R1986,8A100

[8] On the Euler numbers and the distribution of E-irregular primes, preprint, Science University of Tokyo (1984).

[9] On the first case of Fermat's last theorem, II, Manuscripta Math., 56 (1986),no. 4, 465-474.
Z591.10012; 599.10012; M87k:11032; R1987,4A93

[10] On Bernoulli Numbers, I, C.R. Math. Rep. Acad. Sci. Canada, 10 (1988), 7-12.
Z645.10014; M89c:11034; R1988,10A108

[11] On Bernoulli and Euler numbers, Manuscr. Math., 61 (1988), 1-10.
Z648.10007; M89i:11030; R1988,10A109

[12] A note on unit and class number of real quadratic fields, Acta Math. Sinica (N.S.), 5 (1989), no. 3, 281-288.
Z701.11045; M90i:11124; R1990,9A265

[13] On Bernoulli numbers, II, Sichuan Daxue Xuebao, 26 (1989), Special Issue, 60-65.
Z707.11018; M91g:11018

[14] On Fermat's last theorem, C.R. Math. Rep. Acad. Sci. Canada, 12 (1990), no. 1, 11-15.
Z703.11015; M91f:11017; R1990.10A91

[15] On the Kummer-Mirimanoff congruences, Acta Arith., 55 (1990), no. 2, 141-156.
Z(648.10013)688.10014; M91d:11020; R1991,2A102

[16] Some variations and consequences of the Kummer-Mirimanoff congruences, Acta Arith. 62 (1992), no.1, 73-96.
Z738.11031;780.11015; M93i:11035; R1993,4A130

[17] On the Kummer system of congruences and the Fermat quotients, Exposition. Math., 12 (1994), no. 3, 243-253.
Z813.11009; M95g:11020

[18] On Giuga's conjecture, Manuscripta Math., 87 (1995), no. 4, 501-510.
Z845.11004; M96f:11005

[19] On Fermat and Wilson quotients, Exposition. Math., 14 (1996), no. 2, 145-170.
Z857.11001; M97e:11008

[20] Stickelberger subideals for a prime modulus related to Kummer-type congruences, J. Number Theory, 67 (1997), no. 2, 203-214.
Z898.11042; M98k:11171

[21] Stickelberger subideals related to Kummer-type congruences, Math. Slovaca 48 (1998), no. 4, 347-364.
M2000c:11180

AGOH T., DILCHER K., SKULA L.,
[1] Fermat quotients for composite moduli, J. Number Theory 66 (1997), no. 1, 29-50.
Z884.11003; M98h:11002

[2] Wilson quotients for composite moduli, Math. Comp. 67 (1998), no. 222, 843-861.
Z980.13202; M98h:11003

AGOH T., MORI K.,
[1] Kummer type systems of congruences and bases of Stickelberger subideals, Arch. Math. (Brno), 32 (1996), no. 3, 211-232.
Z903.11007; M98h:11132; R1998,4A230

AGOH T., SHOJI T.,
[1] Quadratic equations over finite fields and class numbers of real quadratic fields, Monatsh. Math. 125 (1998), no. 4, 279-292.
Z898.11043; M99b:11120

AGOH T., SKULA L.,
[1] Kummer type congruences and Stickelberger subideals, Acta Arith., 75 (1996), no. 3, 235-250.
Z841.11012; M97j:11052; R1997,8A241

AGRAWAL B.D., PRASAD J.,
[1] Extension of the Bernoulli numbers and polynomials, Bull. Math. Soc. Sci. Math. R.S. Roumaine (N.S.) (1982), 26 (74), no. 3, 211-215.
Z499.33010; M83k:33026; R1983,3V465

AINSWORTH O.R.,
[1] On generating functions, Fibonacci Quart., 15 (1977), no. 2, 161-163.
Z362.40003; M56#2840; R1978,3B37

AINSWORTH O.R., NEGGERS J.,
[1] A family of polynomials and powers of the secant, Fibonacci Quart. 21 (1983), no. 2, 132-138.
Z541.10011; M84k:33001

AKHIEZER N.I.: see STIEIRMAN I.JA., AKHIEZER N.I.

ALBADA P.J. van,
[1] The Bernoulli numerators, EUT Report-WSK, Eindhoven 84-WSK-03, (1984), 1-5.
Z557.10012; R1985,4V489

ALLENBY R.B.J.T., REDFERN E.J.,
[1] Introduction to number theory with computing, Edward Arnold, London-Melbourne- Auckland, 1989. x + 310 pp.
Z681.10001; M90k:11001

ALMKVIST G.,
[1] Wilf's conjecture and a generalization, In: The Rademacher legacy to mathematics (University Park, PA, 1992), 211-233, Contemp. Math., 166, Amer. Math. Soc., Providence, RI, 1994.
Z809.11026; M95g:11032

ALMKVIST G., GRANVILLE A.,
[1] Borwein and Bradley's Apéry-like formulae for $\zeta(4n+3)$, Experiment. Math. 8 (1999), no. 2, 197-203.

ALMKVIST G., MEURMAN A.,
[1] Values of Bernoulli polynomials and Hurwitz's zeta function at rational points, C. R. Math. Rep. Acad. Sci. Canada, 13 (1991), no. 2-3, 104- 108.
Z731.11014; M92g:11023; R1992,4A62

ALONSO J.,
[1] Arithmetic sequences of higher order, Fibonacci Quart., 14 (1976), no. 2, 147-152.
Z361.10014; M53#5455

AL-SALAM W.A., CARLITZ L.,
[1] Bessel polynomials and Bernoulli numbers, Arch. Math., 9 (1958), 412-415.
Z82.286; M21#3597; R1960,3182

[2] Bernoulli numbers and Bessel polynomials, Duke Math. J., 26 (1959), no. 3, 437-445.
Z92.292; M21#4256; R1960,9112

[3] Some determinants of Bernoulli, Euler and related numbers, Portugal. Math., 18 (1959), 91-99.
Z93.15; M23#A848; R1961,1B348

ALVARADO R., PEDRO,
[1] Sums of powers and Bernoulli numbers (Spanish), Rev. Mat. Dominicana, No. 1-2 (1986), 29-36.
M93f:11018

ALZER H.,
[1] Ein Duplikationstheorem für die Bernoullischen Polynome, Mitteilungen Math. Ges. Hamburg, 11 (1987), no. 4, 469-471.
Z632.10008; M88m:11009; R1988,7B20

[2] Inequalities for non-decreasing sequences, Proc. Royal Soc. Edinburgh, Sect. A, 123 (1993), no. 6, 1017- 1020.
Z799.26018; M95b:26021

[3] On some inequalities for the Gamma and psi functions, Math. Comp. 66 (1997), no. 217, 373-389.
Z854.33001; M97e:33004; R1997,4B94

[4] Sharp bounds for the Bernoulli numbers, Arch. Math. (Basel) 74 (2000), no. 3, 207-211.

AMICE Y.,
[1] Sur une conjecture de Leopoldt, Colloq. Algèbre, Ecole norm. supér. jeunes filles (1967), Paris (1968) 9/01-9/08.
R1969,7A294

[2] Une démonstration analytique p-adique du théorème de Ferrero-Washington, d'après Daniel Barsky, Séminaire de théorie des nombres, Paris (1982/83), Birkhäuser Boston, Boston, Mass., 1984, 1-20.
Z546.12010; M87b:11108; R1985,8A203

AMICE Y., FRESNEL J.,
[1] Fonctions zeta p-adiques des corps de nombres abeliens réels, Acta Arith., 20 (1972), 353-384.
Z217,43(237.12010); M49#2667; R1973,2A328

AMSLER R.,
[1] Sur les polynomes de Bernoulli, Bull. Soc. Math. France, 56 (1928), II, 36-41.
J54.485

ANASTASSIADIS J.,
[1] Définition fonctionnelle des polynômes de Bernoulli et d'Euler, C.R. Acad. Sci. Paris, 258 (1964), 1971-1973.
Z124,34; M28#4162; R1964,11B48

ANDO TETSUYA,
[1] The Riemann-Roch theorem and Bernoulli polynomials, Proc. Japan. Acad., A 61 (1985), no. 6, 161-163.
Z607.14008; M87a:14017; R1985,12A416

ANDRÉ D.,
[1] Développements de $\sec x$ et de $\tan x$, C.R. Acad. Sci. Paris, 88 (1879), 965-967.

ANDREWS G., FOATA D.,
[1] Congruences for the $q$-secant numbers, European J. Combin., 1 (1980), no. 4, 283-287.
Z455.10006; M82d:05018

ANDREWS G., GESSEL I.,
[1] Divisibility properties of the q-tangent numbers, Proc. Amer. Math. Soc., 68 (1978), no. 3, 380-384.
Z401.10020; M57#2925; R1978,12A131

ANKENY N.C., ARTIN E., CHOWLA S.,
[1] The class-numbers of real quadratic fields, Proc. Nat. Acad. Sci. U.S.A., 37 (1951), 524-527.
Z43,40; M13-212c

[2] The class-numbers of real quadratic number fields, Ann. of Math., 56 (1952), 479-493.
Z49,306; M14-251h

ANKENY N.C., CHOWLA S.,
[1] Note on the class-number of real quadratic fields, Acta Arith., 6 (1960), 145-147.
Z93,43; M22#6780; R1961,7A125

[2] A further note on the class-number of real quadratic fields, Acta Arith., 7 (1962), 271-272.
Z214,308; M25#1147; R1963,1A137

AOKI N.,
[1] On the Stickelberger ideal of a composite field of some quadratic fields, Max-Planck-Institut für Math. Bonn, MPI/90-16, 24 pp., 1990.

[2] On the Stickelberger ideal of a composite field of quadratic fields, Comm. Math. Univ. St. Paul., 39 (1990), no. 2, 195-209.
Z728.11055; M91m:11091

APOSTOL T.M.,
[1] Generalized Dedekind sums and transformation formulae of certain Lambert series, Duke Math. J., 17 (1950), no. 2, 147-157.
Z39,038; M11-641g

[2] On the Lerch zeta function, Pacific J. Math., 1 (1951), 161-167.
Z43,71; M13-328b

[3] Theorems on generalized Dedekind sums, Pacific J. Math., 2 (1952), no. 1, 1-19.
Z47,45; M13-725c

[4] Quadratic residues and Bernoulli numbers, Delta (Waukesha), 1 (1968/1970), no. 4, 21-31.
Z249.10006; M42#188

[5] Dirichlet $L$-functions and character power sums, J. Number Theory 2 (1970), 223-234.
Z198.37502; M41#3412; R1970,12A85

[6] Another elementary proof of Euler's formula for $\zeta(2n)$, Amer. Math. Monthly, 80 (1973), 425-431.
Z267.10050; M47#3330

[7] Introduction to analytic number theory, Springer-Verlag, New York, 1976. xii + 338 pp.
Z335.10001; M55#7892; R1977,1A98K

[8] Modular functions and Dirichlet series in number theory, Springer-Verlag, New York, 1976. x + 198 pp.
[9] An elementary view of Euler's summation formula, Amer. Math. Monthly, 106 (1999), no. 5, 409--418.

Z332.10017; M54#10149; R1977,5A73K

APOSTOL T.M., VU THIENNU H.,
[1] Dirichlet series related to the Riemann zeta function, J. Number Theory, 19 (1984), no. 1, 85-102.
Z539.10032; M85j:11106; R1985,1A165

APPELL P.,
[1] Sur les fonctions de Bernoulli à deux variables, Arch. Math. und Phys. (3), 4 (1902), 292-293.
J34.484

[2] Sur les polynômes qui expriment la somme des puissances $p^ièmes$ des $n$ premiers nombres entiers, Nouvelles Ann. Math. (3), 6 (1887), 312-321.

[3] Sur les valeurs approchées des polynômes de Bernoulli, Nouv. Ann. Math. (3), 6 (1887), 547-554.
J19.240

ARAKAWA T.,
[1] Dirichlet series $\sum_{n=1^\infty cot(\pi n \alpha)/n^j$, Dedekind sums, and Hecke L-functions for quadratic fields, Comm. Math. Univ. St. Paul., 37 (1988), 209-235.
Z667.12006; M89i:11124

[2] Special values of L-functions associated with the space of quadratic forms and the representations of $S_p(2n, F_p)$ in the space of Siegel cusp forms. In: Automorphic forms and geometry of arithmetic varieties, 99-169, Adv. Stud. Pure Math., 15 , Academic Press, Boston, MA, 1989.
Z701.11018; M91f:11037

[3] Minkowski-Siegel's formula for certain orthogonal groups of odd degree and unimodular lattices, Comment. Math. Univ. St. Paul. 45 (1996), no. 2, 213-227.
Z873.11030; M97i:11075

ARAKAWA T., KANEKO M.,
[1] Multiple zeta values, poly-Bernoulli numbers, and related zeta functions, Nagoya Math. J. 153 (1999), 189-209.
M2000e:11113

[2] On poly-Bernoulli numbers, Comment. Math. Univ. St. Paul. 48 (1999), no. 2, 159-167.

ARAMBURU J.M. ORTEGA: see ORTEGA ARAMBURU J.M.

ARFWEDSON G.,
[1] Om Bernoullis tal och teorem, Elementa matem. fysik kemi, 71 (1988), 83-88.
R1988.12A84

ARKIN J., HOGGATT V.E.,
[1] The generalized Fibonacci numbers and its relation to Wilson's theorem, Fibonacci Quart., 13 (1975), no. 2, 107-110.
Z303.10011; M50#12900; R1975,10V247

ARLETTAZ D.,
[1] Die Bernoulli-Zahlen: eine Beziehung zwischen Topologie und Gruppentheorie. (German) [The Bernoulli numbers: a relation between topology and group theory], Math. Semesterber. 45 (1998), no. 1, 61-75.
Z892.55001; M99e:55012

ARNDT F.,
[1] Über bestimmte Integrale, Arch. Math. und Phys. (1), 6 (1845), 434-439.

[2] Entwicklung der Summen der n-ten Potenzen der natürlichen Zahlen nach den Potenzen des Index mittels des Taylor'schen Lehrsatzes, J. Reine Angew. Math., 31 (1846), 249-252.

[3] Über die Summirung der beiden Reihen (a) $\gamma_0 - n_1 \gamma_1 + n_2 \gamma_2 -$ etc. $ + (-1)^n \gamma_n$, (b) $\gamma_0 + n_1 \gamma_1 + n_2 \gamma_2 +$ etc. $ + \gamma_n$, in welchen die Grössen $\gamma$ willkührlich und die Coefficienten Binomialcoefficienten des ganzen Exponenten $n$ sind, mittels höherer Differenzen und Summen, J. Reine Angew. Math., 31 (1846), 235-245.

[4] Über die Bernoulli'sche Methode, summirbare Reihen zu finden, J. Reine Angew. Math., 31 (1846), 253-258.

ARNOL'D V.I.,
[1] Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetic, Duke Math. J., 63 (1991), no. 2, 537-555.
Z755.58015; M93b:58020

[2] Congruences for Euler, Bernoulli and Springer numbers of Coxeter groups. (Russian), Izv. Ross. Akad. Nauk Ser. Mat., 56 (1992), no. 5, 1129-1133. Engl. Transl. in: Russian Acad. Sci. Izv. Math., 41 (1993), no.2, 389-393.
Z801.11012; M94a:11024; R1993,5A167

[3] Snake calculus and the combinatorics of the Bernoulli, Euler and Springer numbers of Coxeter groups. (Russian), Uspekhi Mat. Nauk, 47 (1992), no. 1(283), 3-45. Translation in Russian Math. Surveys 47 (1992), no. 1, 1-51.
Z791.05001, 801.11012; M93h:20042

ARTIN E.: see ANKENY N.C., ARTIN E., CHOWLA S.

ATKINSON M.D.,
[1] How to compute the series expansions of $\sec x$ and $\tan x$, Amer. Math. Monthly 93 (1986), 387-389
Z603.65013; R1988,1G67

AUCOIN A.A.,
[1] On harmonic series and Bernoulli numbers, Tex. J. Sci., 27 (1976), no. 4, 411-414.
R1977,12V596

AYOUB R.,
[1] Euler and the zeta function, Amer. Math. Monthly, 81 (1974), 1067-1086.
Z293.10001; M50#12566; R1975,8A17


BABADGANJAN R.S.,
[1] Ob ostatochnom chlene v formule Ejlera-Maklorena (Russian) [On the remainder term in the Euler-Maclaurin formula]. Leningr. Gos. Pedagog. In-t., Leningrad, 1986, 14 str.
R1986,7A18DEP

[2] K istorii odnogo funktsional'nogo uravneniya Ejlera (Russian) [On the history of a functional equation of Euler]. Leningr. Gos. Pedagog. In-t., Leningrad, 1986, 6 str.
R1986,7A19DEP

BABBAGE CH.,
[1] On some new methods of investigating the sums of several classes of infinite series, Philos. Trans. Roy. Soc. London, (1819), 249-282.

BABINI J.,
[1] Polinomios generalizades de Bernoulli y sus correlativos, Boletiín Sem. mat. Argentino, 4 (1934), 23-25. and Rev. mat. hisp-amer. (2), 10 (1934), 23-25.
J60.II.1041, 61.II.1166; Z11,213

[2] Generalización de los polinomios de Bernoulli, Rev. Acad. Sci. Madrid, 32 (1935), 491-500.
J61.I.378; Z13,167

BACHMANN P.,
[1] Niedere Zahlentheorie, Additive Zahlentheorie, Leipzig, 1910 / New York: Chelsea, 1968, Part 1: x+402p; Part II: x+480p.
J41.221 ; Z253.10001* ; M39#25

[2] Das Fermatproblem in seiner bisherigen Entwicklung, Walter de Gruyter & Co., Berlin-Leipzig, 1916, 160pp.
J47.105

[3] Ein Satz von den Tangentenkoeffizienten, Arch. der Math. u. Physik (3), 16 (1910), 363-365.
J41.223

BAILEY D.H., BORWEIN J.M., CRANDALL R.E.,
[1] On the Khintchine constant. Math. Comp., 66 (1997), no. 217, 417-431.
Z854.11078; M97c:11119

BAILEY D.H., BORWEIN J.M., GIRGENSOHN R.,
[1] Experimental evaluation of Euler sums. Experiment. Math., 3 (1994), no. 1, 17-30.
Z810.11076; M96e:11168

BAKER Alan,
[1] A Concise Introduction to the Theory of Numbers, Cambridge University Press, Cambridge, 1984. xiii + 95 pp.
Z554.10001; M86f:11001

BAKER A.J., CLARKE F., RAY N., SCHWARTZ L.,
[1] On the Kummer congruences and the stable homotopy of BU, Trans. Amer. Math. Soc., 316 (1989), no. 2, 385-432.
Z709.55012; M90c:55003; R1990,12A606

BAKER Andrew,
[1] A supersingular congruence for modular forms, Acta Arith. 86 (1998), no. 1, 91-100.
M99j:11066

BAKHMUTSKAYA E.Ya.,
[1] Dzhon Blissard i ego simvolicheskoye ischisleniye [John Blissard and his symbolic calculus], Trudy XIII mezhdunarodnogo kongressa po istorii nauki, sek. 5, 1971, 121-124. Nauka, Moskva, 1974.
Z296.01015; R1975,1A44

BALAN G.,
[1] Group of unit of cyclotomic field, In: Proc. Conference on Algebra. Univ. of Cluj-Napoca, Faculty of Math., Research Seminars. Preprint No. 9, 1986, 3-6.
Z691.12001; R1987,5A317

BALATONI F.,
[1] On the class number of quadratic number fields (Hungarian), Math. Lapok, (1973), 107-112.
Z326.12004 ; M53#5527; R1976,6A179

BALAZS N.L., SCHMIT C., VOROS A.,
[1] Spectral fluctuations and zeta functions, J. Statistical Physics, 46 (1987), no. 5/6, 1067-1090.
Z692.58027; M89b:58171

BALK M.B.,
[1] A property of the Bernoulli numbers. (Russian), Moskov. Oblast. Pedagog. Inst. Uch. Zap., 57 (1957), 55-59.
Z90,279 ; M20#5892; R1958,7462

BALOG A., DARMON H., ONO K.,
[1] Congruence for Fourier coefficients of half-integral weight modular forms and special values of $L$-functions. Analytic number theory, Vol. 1 (Allerton Park, IL, 1995), 105-128, Progr. Math., 138, Birkhduser Boston, Boston, MA, 1996.
Z863.11031; M97e:11056

BANASZAK G., GAJDA W.,
[1] On the arithmetic of cyclotomic fields and the $K$-theory of ${\bf Q}$, Algebraic $K$-theory Poznan, 1995), 7-18, Contemp. Math., 199, Amer. Math. Soc., Providence, RI, 1996.
Z866.19004; M97h:11146

BANERJEE D.P.,
[1] On some arithmetical properties of Bernoulli's and Euler's generalized polynomials, Proc. Indian Nat. Sci. Acad. Part A, 34 (1964), 92-96.
Z171.32601; M36#2851; R1965,6V50

BANUELOS A., DEPINE R.A.,
[1] A program for computing the Riemann zeta function for complex argument, Comput. Phys. Comm., 20 (1980), 441-445.
Z457.10001; R1981,5V1033

BARANIECKI M.A.,
[1] O funkcyjach Bernoulliego. Kraków, Ak. (Mat.-Przyrod.) Rozpr. 13 (1886), 183-195.
J1885,416

BARNER K.,
[1] Über die Werte der Ringklassen-L-Funktionen reell-quadratischer Zahlkörper an natürlichen Argumentstellen, J. Number Theory, 1 (1969), no. 1, 28-64.
Z174,86; M39#139; R1970,2A127

BARNES E. W.,
[1] The theory of the gamma function, Messenger Math. (2), 29 (1899/1900), 64-128.
J30.389

[2] The theory of the double gamma function, Philos. Trans. London, 196A (1901), 271-285.
J32.442

[3] On the theory of the multiple gamma function, Trans. Cambr. Philos. Soc., 19 (1904), 374-425.
J35.462

BARNIVILLE J.J., DICKSON J.D.H., LAMPE E.,
[1] Solution of question 9977, Math. questions etc., edited by W.J.C. Miller, London, 52 (1890), 41-44.
J22.268

BARSKY D.,
[1] Analyse p-adique et nombres de Bernoulli, C.R. Acad. Sci. Paris, 283 (1976), no. 16, A1069-A1072.
Z359.12018 ; M55#2855; R1977,7A339

[2] Congruences de coefficients de séries de Taylor (Application aux nombres de Bernoulli-Hurwitz), Groupe d'étude d'analyse ultramétrique, no. 17, (1975-76), 9pp.
Z355.12016; M58#5496; R1978,3A300

[3] Fonction génératrice et congruences (Application aux nombres de Bernoulli), Sém. Délange-Pisot-Poitou (Théorie de nombres), 1975-76 (1977), 17, fasc. 1, exp. 21, 16pp.
Z336.12012 ; M57#5967; R1978,3A235

[4] Analyse p-adique et nombres de Bernoulli-Hurwitz, C.R. Acad. Sci. Paris, 284 (1977), no. 3, A137-A140.
Z343.12007; M55#12705; R1977,10A208

BARSKY D., DUMONT D.,
[1] Congruences pour les nombres de Genocchi de deuxième espèce, Seminaire du groupe d'étude d'analyse ultramétrique, 34 (1980-81), 1-13.
Z474.10011; M82m:10021; R1982,1V747

BARTZ K.,
[1] On Carlitz theorem for Bernoulli polynomials. Number theory (Cieszyn, 1998). Ann. Math. Sil. No. 12 (1998), 9-13.
Z924.11009; M2000a:11030

BARTZ K., RUTKOWSKI J.,
[1] On the von Staudt-Clausen theorem, C. R. Math. Rep. Acad. Sci. Canada, 15 (1993), no. 1, 46-48.
Z769.11011; M94b:11017; R1993,11A101

BASKOV B.M.,
[1] Svyaz' dzeta-funktsii Rimana s mnogochlenami Bernulli (Russian) [Connection between the Riemann zeta function and the Bernoulli polynomials]. Trudy Uzbeksk. Gos. Universiteta, novaya ser., fiz.-mat. fakul't., Samarkand, (1958), no. 78, 163-183.
R1962,5A127

[2] Novoe dokazatel'stvo teoremy Shtaudta (Russian) [A new proof of Staudt's theorem]. Materialy 3-i ob'ed. nauch. konf. uchenykh Samarkanda, ser. gumanit. i estest. nauk, Samarkand, (1961), 260-262.
R1963,3A140

BATEN W. D.,
[1] A remainder for the Euler-Maclaurin summation formula in two independent variables, Amer. J. Math., 54 (1932), 265-275.
J58.II.1044; Z4.250

BAUER G.,
[1] Von den Gamma-functionen und einer besonderen Art unendlicher Producte, J. Reine Angew. Math., 57 (1860) , 256-272.

[2] Von einigen Summen-und Differenzenformeln und den Bernoullischen Zahlen, J. Reine Angew. Math., 58 (1861), 292-300.

BAYAT M.,
[1] A generalization of Wolstenholme's theorem, Amer. Math. Monthly 104 (1997), no. 6, 557-560.
Z970.65389; M98e:11007

BÁYER P.,
[1] Value of the Iwasawa L-function at point $s=1$, Arch. Math., 32 (1979), no. 1, 38-54.
Z403.12022; M80h:12016 ; R1980,2A374

[2] Sobre el indice de irregularidad de los numeros primos, Collect. Math., 30 (1979), no. 1, 11-20, (Spanish).
Z499.12003; M81h:12003

[3] Variae observationes circa series infinititas, Butlleti Soc. Catalana Ciénc. Fis., Quimiques i Matem., 2 (1984), no. 4, 429-481.
Z598.10002; M86i:01026

BEACH B., WILLIAMS H., ZARNKE C.,
[1] Some computer results on units in quadratic and cubic fields, Proc. of the Twenty-Fifth Summer Meeting of the Canad. Math. Congress, Lakehead Univ., (1971), 609-648.
M49#2656

BEARDON A. F.,
[1] Sums of powers of integers. Amer. Math. Monthly, 103 (1996), no. 3,201-213 .
Z851.11012; M97f:11020; R1996,10B189

BEEBEE J.,
[1] Bernoulli numbers and exact covering systems, Amer. Math. Monthly, 99 (1992), no. 10, 946-948.
Z776.11008; M93i:11025; R1993,8A109

BEEGER N.W.G.H.,
[1] Quelques remarques sur les congruences $\tau^{p-1 \equiv 1 (\bmod p^2)$ et $(p - 1)! \equiv (\bmod p^2)$, Messeng. Math. (2), 43 (1913), 72-84.
J44.227

[2] On some new congruences in the theory of Bernoulli numbers, Bull. Amer. Math. Soc., 44 (1938), 684-688.
J64.II.96; Z19.292

[3] Report on some calculations of prime numbers, Nieuw Arch. Wisk., 20 (1939), 48-50.
J65.161; Z20.105; M1-65g

BEESLEY E.M.,
[1] An integral representation for the Euler numbers, Amer. Math. Monthly, 76 (1969), 389-391.
Z185,30; M39#4330; R1970,3V274

BELL E.T.,
[1] The Bernoullian functions occuring in the arithmetical applications of elliptic functions, Messeng. Math. (2), 50 (1921), 177-186. = Bull Amer. Math. Soc., 27 (1921), 413.
J48.444, 48.1245

[2] Note on the prime divisors of the numerator of Bernoulli's numbers, Amer. Math. Monthly, 28 (1921), 258-259. = Bull. Amer. Math. Soc., 27 (1921), 414.
J48.137, 48.255

[3] Anharmonic polynomial generalizations of the numbers of Bernoulli and Euler, Bull. Amer. Math. Soc., 27 (1921), 414.
J48.255

[4] Anharmonic polynomial generalizations of the numbers of Bernoulli and Euler, Trans. Amer. Math. Soc., 24 (1922), no. 2, 89-112.
J(49.708)

[5] A revision of the Bernoullian and Eulerian functions, Bull. Amer. Math. Soc., 28 (1922), 443-450.
J48.1194

[6] Relations between the numbers of Bernoulli, Euler, Genocchi, and Lucas, Messeng. Math., 52 (1923), 56-68.
J49.328

[7] Umbral symmetric functions and algebraic analogues of the Bernoullian and Eulerian numbers and functions, Bull. Amer. Math. Soc., 29 (1923), 11. = Math. Z., 19 (1924), 35-49.
J49.78, 49.250

[8] An algebra of sequences of functions with an application to the Bernoulli functions, Trans. Amer. Math. Soc., 28 (1926), no. 1, 129-148.
J52.372

[9] General relations between Bernoulli, Euler and allied polynomials, Trans. Amer. Math. Soc., 38 (1935), 493-500.
J61.I.377; Z13.5

[10] The history of Blissard's symbolic method, with a sketch of its inventor's life, Amer. Math. Monthly, 45 (1938), 414-421.
Z19,389

[11] Trigonometry and the numbers B, E, G, R of Bernoulli, Euler, Genocchi and Lucas (Abstract), Bull. Amer. Math. Soc., 28 (1922), 283.
J(48.256)

[12] The modular Bernoullian and Eulerian functions (Abstract ), Bull. Amer. Math. Soc., 32 (1926), 417-418.
J(52.373)

[13] On generalizations of the Bernoullian functions and numbers, Amer. J. Math., 47 (1926), 277-288.
J51.289

[14] B, E polynomials and their related integrals, Tôhoku Math. J, 26 (1926), 391-405.
J53.354

[15] Modular Bernoullian and Eulerian functions, Univ. of Washington Publ. in Math., 1 (1926), no. 1, 1-7.
J57.II.1369

BELL J.L.,
[1] Chains of congruences for the numerators and denominators of the Bernoulli numbers, Ann. of Math. (2), 29 (1927), 106-112.
J53.137

BELLAVITIS G.,
[1] Sulle serie di numeri che comprendono i Bernoulliani, Annali. sci. mat. e fis. Roma, 4 (1853), 108-127.

BENDERSKI L.,
[1] Sur la fonction gamma géneralisée, Acta Math. 61 (1933), 263-322.

BENNETON G.,
[1] Sur le dernier théorème de Fermat, Ann. Sci. Univ. Besançon, Math. (3), fasc. 7 (1974), 15pp.
Z348.10010; M54#7368

BENTSEN S., MADSEN I.,
[1] Trace maps in algebraic $K$-theory and the Coates-Wiles homomorphism, J. Reine Angew. Math., 411 (1990), 171-195.
Z716.11055; M91i:19002

BERG F.J. van den,
[1] Over periodieke terugloopende betrekkingen tusschen de Coëfficiënten in de ontwikkeling van functiën, meer in het byzonder tusschen de Bernoulliaansche en ook tusschen eenige daarmede verwante Coëfficiënten, Versl. Meed. Kon. Ak. Weten., (2), 16 (1881), 74-176 = Arch. Néerl. Sci. Ex. Nat. Soc. Holland., 16 (1881), 387-443.
J13.193

[2] Eenige formulen voor de berekening van de Bernoulliaansche en van de tangenten-coëfficiënten, Verhand. Kgl. Akad. Wetensch. Amsterdam, (3), 5 (1889), 358-397; 6 (1889), 265-276.
J20.265

[3] Quelques formules pour le calcul des nombres de Bernoulli et des coefficients des tangentes, Arch. Néerl. Sci. Exactes et Natur. Soc. Hollandaise, 24 (1891), 99-141.
J22.268

BERGER A.,
[1] Elementära bevis för några formler i differenskalkylen, Handl. Kgl. Svenska Vetens. Akad., Stockholm, 37 (1882), 39-53.
J14.192

[2] De Bernoulli'ska talens och funktionernas teori, baserad på ett system af funktionaleqvationer, Öfversigt af Kgl. Svenska Vetens. Akad. Förhand., Stockholm, 45 (1888), 433-461.
J20.424

[3] Härledning af några independenta uttryck för de Bernoulli'ska talen, Öfversigt af Kgl. Svenska Vetens. Akad. Förhand., Stockholm, 46 (1889), 129-138.
J21.247

[4] Sur une généralisation des nombres et des fonctions de Bernoulli, Bihang Kgl. Svenska Vetens. Akad. handl., Stockholm, 13 (1890), no. 9, 1-43.
J22.266

[5] Recherches sur les nombres et les fonctions de Bernoulli, Acta Math., 14 (1890/91), 249-304.
J23.267

[6] Om en användning af de Bernoulliska funktionerna vid några serienutvecklingar, Öfversigt af Kgl. Svenska Vetens. Akad. Förhandl., Stockholm, 48 (1891), 523-540.
J23.274

BERGER E.R.,
[1] Bernoullische Zahlen, Potenzsummen und Stirlingsche Reihe, Z. Angew. Math. Mech., 35 (1955), 70-71.
Z64,13; M16-1014e; R1956,2302

BERGGREN B.,
[1] Summierung der Reihe $1^n + 2^n + 3^n + \cdots + \nu^n$ (Swedish), Elementa, Stockholm, 22 (1939), 209-212.
J65.1190

BERGMANN H.,
[1] Eine explizite Darstellung der Bernoullischen Zahlen, Math. Nachr., 34 (1967), 377-378.
Z307.10018 ; M36#4030; R1968,6V311

BERNDT B.C.,
[1] Character transformation formulae similar to those for the Dedekind eta-function. In: Analytic number theory (Proc. Sympos. Pure Math., Vol. 24, St. Louis Univ., St. Louis, Mo., 1972), pp. 9-30. Amer. Math. Soc., Providence, R. I., 1973.
Z265.10016; M49#2556

[2] Periodic Bernoulli numbers, summation formulas and applications. In: Theory and application of special functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), pp. 143-189. Math. Res. Center, Univ. Wisconsin, Publ. No. 35, Academic Press, New York, 1975.
Z326.10016; M52#10560; R1978,7B39

[3] Elementary evaluation of $\zeta(2n)$, Math. Mag., 48 (1975), 148-154.
Z303.10038; M51#3078; R1976,5A98

[4] Character analogues of the Poisson and Euler-Maclaurin summation formulas with applications, J. Number Theory, 7 (1975), no. 4, 413-445.
Z316.10023; M52#3075; R1976,6A131

[5] On Eisenstein series with characters and the values of Dirichlet L-functions, Acta Arith., 28 (1975), no. 3, 299-320.
Z279.10023; M52#10601; R1976,8A177

[6] Dedekind sums and a paper of G.H. Hardy, J. London Math. Soc., 13 (1976), 129-137.
Z319.10006; M53#7918; R1976,12A127

[7] Chapter 8 of Ramanujan's second notebook, J. Reine Angew. Math., 338 (1983), 1-55.
Z491.33003; M84g:01080; R1983,7B13

[8] Chapter 11 of Ramanujan's second notebook, Bull. London Math. Soc., 15 (1983), no. 4, 273-320.
Z(494.33002),506.33002; M85a:01043; R1983,12B35

[9] Ramanujan's quarterly reports, Bull. London Math. Soc., 16 (1983), no. 5, 449-489.
Z(511.01007),539.01012; M85j:01021; R1985,4A101

[10] Remarks on some of Ramanujan's number theoretical discoveries found in his second notebook. Number Theory. Proc. 4th Matscience Conf. held at Ootacamund, India, January 5-10, 1984. Lect. Notes Math. No. 1122, Springer-Verlag Berlin-New York, 1985, 47-55.
Z555.10002; M87b:11013; R1985,11A121

[11] Ramanujan's Notebooks. Part I. Springer-Verlag, New York-Berlin, 1985, x + 357 pp.
Z555.10001; M86c:01062; R1986,2B1K

[12] Ramanujan's notebooks. Part IV. Springer-Verlag, New York, 1994. xii+451pp.
Z785.11001; M95e:11028

[13] Ramanujan's notebooks. Part V. Springer-Verlag, New York, 1998. xiv+624pp.
Z886.11001; M99f:11024

BERNDT B.C., BIALEK P.,
[1] Five formulas of Ramanujan arising from Eisenstein series. In: Number Teory (K. Dilcher, Ed.), Fourth Conference of the Canadian Number Theory Association (Halifax, July 2-8, 1994), CMS Conference Proceedings 15, 67-86. Amer. Math. Soc., Providence, 1995.
Z838.40001; M97f:11028; R1997,9A122

BERNDT B.C., EVANS R.J.,
[1] Chapter 7 of Ramanujan's second notebook, Proc. Indian Acad. Sci. Math. Sci., 92 (1983), no. 2, 67-96.
Z537.10002; M86d:11020; R1985,3A95

[2] Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook, J. Reine Angew. Math., 361 (1985), 118-134.
Z571.41027; M87b:41031; R1986,4A125

[3] Chapter 15 of Ramanujan's second notebook. Part II. Modular forms. Acta Arith., 47 (1986), no. 2, 123-142.
Z571.10025; M88d:11039; R1987,5A96

[4] Asymptotic expansion of a series of Ramanujan, Proc. Edinburgh Math. Soc.(2), 35 (1992), no. 2, 189-199.
Z741.41025; M93i:41020

BERNDT B.C., EVANS R.J., WILSON B.M.,
[1] Chapter 3 of Ramanujan's second notebook, Advances in Math., 49 (1983), no. 2, 123-169.
Z524.41017; M85c:11020; R1984,2B41

BERNDT B.C., SCHOENFELD L.,
[1] Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory, Acta Arith., 28 (1975), 23-68. Correction: Acta Arith., 38 (1980/81), 328.
Z(268.10008),311.10018; M52#5586; R1976,5A106

BERNDT B.C., WILSON B.M.,
[1] Chapter 5 of Ramanujan's second notebook. In: Analytic number theory, Lecture Notes in Math., no. 899, Springer-Verlag, 1981, 49-78.
Z477.10003; M83i:10011

BERNDT B.C.: see also ADIGA C., BERNDT B.C., et al.

BERNOULLI J.,
[1] Ars Conjectandi, Basel, (1713). (Reprinted on pp. 106-286 in Vol. 3 of "Die Werke von Jakob Bernoulli", Birkhäuser Verlag, Basel, 1975. See also SMITH D.E. [1, pp. 85-90]).

[2] Wahrscheinlichkeitsrechnung, Leipzig, 1899.

BERNSTEIN F.,
[1] Über den zweiten Fall des letzten Fermatschen Lehrsatzes, Nachr. Akad. Wiss. Göttingen Math.-phys. Kl., (1910), 507-616.
J41.237

BERNSTEIN M., SLOANE N.J.A.,
[1] Some canonical sequences of integers, Linear Algebra Appl., 226-228 (1995), 57-72.
Z832.05002; M96i:05004

BERTRAND J.,
[1] Traité de calcul différentiel et de calcul intégral, Paris, 1 (1864), Ch. 6; 2 (1870), Ch. 7. 507-616.
J2.298

BESSEL R.,
[1] Über die Summation der Progressionen, Astronom. Nachr., 16 (1839), no. 361, 4-6.

BEUKERS F., KOLK J.A.C., CALABI E.,
[1] Sums of generalized harmonic series and volumes, Nieuw Arch. Wisk. (4), 11 (1993), no. 3, 217-224.
Z797.40001; M94j:11022

BEZERRA V.B., CHABA A.N.,
[1] The generalised Euler formula from Poisson's summation formula and some applications, J. Phys. A 18 (1985), no. 17, 3381-3387.
Z596.40002; M87h:65013; R1986,6B17

BHARGAVA S.: see ADIGA C., BERNDT, B.C. et al.

BHARGAVA S.: see ADIGA C., BHARGAVA S.

BHATTACHARJEE N.R.,
[1] Extension of Bernoulli and Euler numbers (Bengali summary), Chittagong Univ. Stud. Part II Sci., 10 (1986), no. 1-2, 13-17.
M90d:11030

BHATTACHARJEE N.R., BHATTACHARJEE T.,
[1] Extension of zeta function $\zeta(2m)$, Indian J. Pure Appl. Math., 21 (1990), no. 11, 977-980.
Z721.11032; M92d:11091

[2] On the evaluation of zeta function $\zeta(2s)$, Indian J. Pure Appl. Math., 23 (1992), no. 1, 15-19.
Z742.11043; M93b:11105; R1992,9A144

BHIMASENA RAO M.: see KRISHNAMACHARY C., BHIMASENA RAO M.

BIALEK P.: see BERNDT B.C., BIALEK P.

BINET M.J.,
[1] Mémoires sur les intégrales définies Euleriennes, Journ. de l'Ecole Polytechn., 16 (1839), 124-343.

[2] Mémoire sur l'application de la théorie des suites à la série des nombres premiers à un nombre composé, C.R. Acad. Sci. Paris, 32 (1851), 918-921.

BIRCH B.J.,
[1] $K_2$ of Global fields, Proc. Sympos. Pure Math., 20 (1971), 87-95.
Z218.83; M48#11052

BISHT C.S.: see SRIVASTAVA H.M., JOSHI J.M.C., BISHT C.S.

BJÖRLING E.G.,
[1] Om de Bernoulliska talen, Öfversigt Kgl. Vetens. Akad. Förhandl., Stockholm, 14 (1857), 107-108.

BLIND A.,
[1] Ueber die Potenzsummen der unter einer Zahl m liegenden und zu ihr primen Zahlen, Dissertation, Bonn 1876 .

BLISSARD J.,
[1] Theory of generic equations, Quart. J. Math., 4 (1861), 279-305; 5 (1862), 58-75, 185-208.

[2] Examples of the use and application of representative notation, Quart. J. Math., 6 (1863), 49-64.

[3] Researches in analysis. I. On the sums of reciprocals, Quart. J. Math., 6 (1864), 242-257.

[4] Researches in analysis. II. On the unlimited variety of result capable of being obtained, by use of Representative Notation, from a single Formula, Quart. J. Pure Appl. Math., 7 (1866), 155-170, 223-226.

[5] On the properties of the $\bigtriangleup^m \bigcirc^n$ class of numbers and of others analogous to them, as investigated by means of representative notation, Quart. J. Math., 8 (1867), 85-110.

[6] Note on a certain formula, Quart. J. Pure Appl. Math. 9 (1868), 71-76.

[7] On the properties of the $\bigtriangleup^m \bigcirc^n$ class of numbers, Quart. J. Pure Appl. Math., 9 (1868), 82-94, 154--171.

BLOOM D. M.,
[1] An old algorithm for the sums of integer powers. Math. Magazine, 66 (1993), no. 5, 304-305.
M94j:11017

BOCK W.,
[1] Eine Beziehung zwischen den Bernoullischen Zahlen und dem Produkt $\Pi (1-1/p^{2n})$ über alle Primzahlen, Mitt. Math. Ges. Hamburg, 5 (1920), 304-307.
J47.219

BÖCHERER S.,
[1] Über die Fourierkoeffizienten der Siegelschen Eisensteinreihen, Manuscripta Math., 45 (1984), no. 3, 273-288.
Z533.10023; M86b:11037; R1984,9A445

BÖHMER P.,
[1] Über die Bernoullischen Functionen, Math. Ann., 68 (1910), no. 3, 338-360.
J41.371

BÖLLING R.,
[1] Bemerkungen über Klassenzahlen und Summen von Jacobi-Symbolen, Math. Nachr., 90 (1979), 159-172.
Z415.12003; M81g:12008; R1980,5A149

BOOLE G.,
[1] Die Grundlehren der endlichen Differenzen- und Summenrechnung. Leibrock, Braunschweig, 1867.

[2] Finite differences, Chapters V-VIII, (1872).

[3] A treatise of the calculus of finite differences, London, (1880), 3rd. ed., Ch. 5-8.

BOREVICH Z.I., SHAFAREVICH I.R.,
[1] Number Theory. Academic Press, New York, 1966. x + 435 pp.
Z121,42; M33#4001

[2] Teoriya chisel [Number Theory], 3rd ed., Nauka, Moscow, 1985, 504 pp.
Z592.12001*; M88f:11001; R1986,1A533K

BORWEIN D., BORWEIN J.M., BORWEIN P.B., GIRGENSOHN R.,
[1] Giuga's conjecture on primality, Amer. Math. Monthly 103 (1996), no. 1, 40-50.
Z860.11003; M97b:11004; R1997,12A58

BORWEIN J.M., BORWEIN P.B.,
[1] Pi and the AGM. A study in analytic number theory and computational complexity. John Wiley & Sons, Inc., New York, 1987.
Z611.10001; M89a:11134

BORWEIN J.M., BORWEIN P.B., DILCHER K.,
[1] Pi, Euler numbers, and asymptotic expansions, Amer. Math. Monthly, 96 (1989), no.8, 681-687.
Z711.11009; M91c:40002

[2] Boole summation and asymptotic expansions of some special series. Conference report of the 9th Czechoslovak Colloquium on Number Theory held at Rackova Dolina, Sept. 1989, pp. 11-18. Masaryk University, Brno, 1990.

BORWEIN J.M., WONG E.,
[1] A survey of results relating to Giuga's conjecture on primality. Advances in mathematical sciences: CRM's 25 years Montreal, PQ, 1994), 13--27, CRM Proc. Lecture Notes, 11, Amer. Math. Soc., rovidence, RI, 1997.
Z980.15140; M98i:11005

BORWEIN J.M.: see also BAILEY D.H., BORWEIN J.M., GIRGENSOHN R.

BORWEIN J.M.: see also BAILEY D.H., BORWEIN J.M., CRANDALL R.E.

BORWEIN J.M.: see also BORWEIN D., BORWEIN J.M., BORWEIN P.B., GIRGENSOHN R.

BORWEIN P.B.: see BORWEIN J.M., BORWEIN P.B.

BORWEIN P.B.: see BORWEIN J.M., BORWEIN P.B., DILCHER K.

BORWEIN P.B.: see also BORWEIN D., BORWEIN J.M., BORWEIN P.B., G IRGENSOHN R.

BOYD, D.W.,
[1] A $p$-adic study of the partial sums of the harmonic series, Experiment. Math. 3 (1994), no. 4, 287-302.
Z838.11015; M96e:11157

BOYER C. B.,
[1] Pascal's formula for the sum of powers of the integers, Scripta Math., 9 (1943), 237-244.
Z60.009; M6-85d

BRADLEY D.,
[1] A sieve auxiliary function. Analytic number theory, Vol. 1 (Allerton Park, IL, 1995), 173-210, Progr. Math., 138, Birkhduser Boston, Boston, MA, 1996.
Z856.11045; M97h:11099

BREMEKAMP H.,
[1] Vraagstuk CXIII, Wiskundige Opgaven, 14 (1928), 238-240.
J54.186

BRENEV E.E.,
[1] O nekotorykh sootnosheniyakh svyazyvayushchikh dzeta-funktsiyu Rimana s polinomami Bernulli [On some relations between the Riemann zeta function and Bernoulli polynomials]. Trudy Moskovsk. instituta inzhenerov zh.-d. transporta, (1966), no. 230, 77-98.< br> R1967,11A141

BRENT B.,
[1] Quadratic minima and modular forms, Experiment. Math. 7 (1998), no. 3, 257-274.

BRILLHART J.,
[1] On the Euler and Bernoulli polynomials, J. Reine Angew. Math., 234 (1969), 45-64.
Z167,354 ; M39#4117; R1969,8B176

[2] Some modular results on the Euler and Bernoulli polynomials, Acta Arith., 21 (1972), 173-181.
Z(213,55),241.10008; M46#3433; R1973,4A194

[3] On the Euler and Bernoulli polynomials. Dissertation, Univ. of California, Berkeley, 1967.
R1986,7V288D

BRINDZA B.,
[1] On some generalizations of the Diophantine equation $1^k+2^k+ \cdots +x^k = y^z$, Acta Arith., 44 (1984), no. 2, 99-107.
Z(497.10010)544.10013; M86j:11029; R1985,7A188

[2] Power values of sums $1^k+2^k+ \cdots +x^k$, Number Theory, Vol. II (Budapest, 1987), 595-611, Colloq. Math. Soc. Jànos Bolyai, 51, Noth-Holland, Amsterdam-New York, 1990.
Z705.11013; M91g:11027; R1992,6A143

BRINDZA B., PINTÉR Á.,
[1] On equal values of power sums, Acta Arith., 77 (1996), no. 1, 97-101.
Z960.51219; M97e:11040; R1997,3A54

BRINKLEY J.,
[1] An investigation on the general term of an important series in the inverse method of finite differences, Phil. Trans. Royal Soc. London, (1807), part 1, 114-132.

BROCARD H.,
[1] Solutions des questions proposées (138, 139), Nouv. Corres. Math., 5 (1879), 282-285.

BRÖDEL W.,
[1] Zum von-Staudtschen Primzahlsatz, Wiss. Z. Friedrich-Schiller-Univ. Jena, Math.-Nat. Reihe, 10 (1960-61), no. 1-2, 21-23.
M23#A3701; R1962,1A143

BRUCKMAN P.S.,
[1] The generalized totient function (Problem #6446, solution by O.P. Lossers), Amer. Math. Monthly, 92 (1985), no. 6, 434-435.
Z679.10011; R1987,11A91

BRÜCKNER H.,
[1] Explizites Reziprozitätsgesetz und Anwendungen, Vorlesungen Fachbereich Math. Univ. Essen, Heft 2, (1979), 83pp.
Z437.12001; M80m:12015

BRUGGEMAN R.W.,
[1] Automorphic forms. In: Elementary and analytic theory of numbers (Warsaw, 1982), 31-74, Banach Center Publ., 17, PWN, Warsaw, 1985.
Z589.10028; M87h:11037

BRUMER A.,
[1] Travaux récent D'Iwasawa et de Leopoldt, Séminaire Bourbaki, 19e année, 325 (1966/67) (1968), 1-14.
Z191,335

BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.,
[1] En brevveksling om et polynom som er i slekt med Riemanns zetafunksjon [Correspondence about a polynomial which is related to Riemann's zeta function], Norsk Mat. Tidsskr. 28, (1946). 65-71.
Z063.00643; M87h:11037

DE BRUYN G.F.C.,
[1] Formulas for $a+a^2 2^p+a^3 3^p+\cdots+a^n n^p$. Fibonacci Quart. 33 (1995), no. 2, 98-103.
Z827.05003; M96e:11026

DE BRUYN G.F.C., DE VILLIERS J.M.,
[1] Formulas for $1+2^p+3^p+\ldots +n^p$. Fibonacci Quart., 32 (1994), no.3, 271-276.
Z803.11017; M95f:11012

BUCHHEIM A.,
[1] Some applications of symbolic methods. [Sect. (3): Staudt's Theorem on Bernoulli's numbers]. Messenger of Math. 11 (1882), 143-145.

BUCKHOLTZ T.J.: see KNUTH D.E., BUCKHOLTZ T.J.

BUDMAMI P.,
[1] Über die Bernoullischen Zahlen (Croatian), Arbeiten der südslavischen Akademie von Agram, Kroatien, 183 (1910), 177-199.
J(41.302)

BUGAEV N.V.,
[1] Uchenie o chislovykh proizvodnykh [Studies on numerical derivatives](Russian). Mat. Sbornik, I, 5 (1870), 1-63; 6 (1872/73), 133-180, 201-254, 309-360.
J3.75

[2] Svojstvo odnogo chislovogo integrala po delitelyam i ego razlichnye primeneniya, logarifmicheskie chislovye funktsii [A property of a numerical integral with regard to divisors and its various applications] (Russian). Mat. Sbornik, I, 13 (1888), 757-777.
J20.186

BUHLER J.P., CRANDALL R.E., ERNVALL R., METSÄNKYLÄ T.,
[1] Irregular primes and cyclotomic invariants to four million. Math. Comp., 61 (1993), no. 203, 151-153.
Z789.11020; M93k:11014

BUHLER J.P., CRANDALL R.E., SOMPOLSKI R.W.,
[1] Irregular primes to one million. Math. Comp. 59 (1992), no. 200, 717-722.
Z768.11009; M93a:11106; R1994,2A84

BUHLER J.P., GROSS B.H.,
[1] Arithmetic on elliptic curves with complex multiplication, II, Invent. Math., 79 (1985), no. 1, 11-29.
Z584.14027; M86j#11066; R1985,7A478

BUHLER J.P.: see also CRANDALL R.E., BUHLER J.P.

BUKHSHTABER V.M.,
[1] The $J$-functor on cellular complexes. (Russian), Dokl. Akad. Nauk SSSR., 170 (1966), 17-20.
Z153.251; M36#3346; R1967,1A341

BURAU W.,
[1] Staudt, K. G. Ch. In: Dictionary of Scientific Biography (Ch. C. Gillespie, Edit. in Chief), Council of Learned Societies, Ch. Scribner's Son, New York, 1976. Vol. 13, 4-6.

BURROWS B.L., TALBOT R.F.,
[1] Sums of powers of integers, Amer. Math. Monthly, 91 (1984), no. 7, 394-403.
Z553.05006; M85j:11018; R1985,5A116

BURSTALL F.W.,
[1] Congrunces se rapportant aux nombres de Bernoulli et d'Euler au module $p^{i+1}$, J. Math. Pures Appl. (7), 3 (1917), 247-261.
J46.189

BUSK Th.,
[1] On some general types of polynomials in one, two or n variables, Ejnar Munksgaard, Copenhagen, 1955, 228p.

BUTZER P.L., FLOCKE S., HAUSS M.,
[1] Euler functions $E_\alpha(z)$ with complex $\alpha$ and applications. In: Approximation, probability and related fields (Santa Barbara, CA, 1993), 127-150, Plenum, New York, 1994.
M96b:33013

BUTZER P.L., HAUSS M.,
[1] On Stirling functions of the second kind, Stud. Appl. Math., 84 (1991), no. 1, 71-91.
Z738.11025; M92k:11023

BUTZER P.L., HAUSS M., LECLERC M.,
[1] Bernoulli numbers and polynomials of arbitrary complex indices, Appl. Math. Lett., 5 (1992), no. 6, 83-88.
Z768.11010; M96c:11023

[2] Extensions of Euler polynomials to Euler functions $E_\alpha(z)$ with complex indices. Pre-print, Lehrstuhl A für Mathematik, RWTH Aachen, 1992.

BUTZER P.L., MARKETT C., SCHMIDT M.,
[1] Stirling numbers, central factorial numbers, and representations of the Riemann zeta-function, Resultate Math., 19 (1991), no. 3-4, 257-274.
Z724.11038; M92a:11095

BUTZER P.L., SCHMIDT M.,
[1] Central factorial numbers and their role in finite difference calculus and approximation, In: Colloq. Math. Soc. János Bolyai, 58 (1990), (Proc. Conf. on Approximation Theory, Kecskemét, Hungary, Aug. 5-11, 1990), 127-150.
Z784.41028; M94c:41007; R1997,2A84

BUTZER P.L., SCHMIDT M., STARK E.L., VOGT L.,
[1] Central factorial numbers; their main properties and some applications, Numer. Funct. Anal. Optim., 10 (1989), no. 5-6, 419-488.
Z659.10012; M90d:05007; R1990,2V334

BYRD P.F.,
[1] New relations between Fibonacci and Bernoulli numbers, Fibonacci Quart., 13 (1975), 59-69.
Z297.10007 ; M51#12684; R1975,10V245

[2] Relations between Euler and Lucas numbers, Fibonacci Quart., 13 (1975), no. 2, 111-114.
Z301.10013; M50#9771; R1975,11V322


CALABI E.: see BEUKERS F., KOLK J.A.C., CALABI E.

CALLAN D.,
[1] Letter to the editor: "A new approach to Bernoulli polynomials" by D.H. Lehmer, Amer. Math. Monthly, 96 (1989), no.6, 510.
M90g:11024

CALLANDREAU O.,
[1] Sur la formule sommatoire de Maclaurin, C.R. Acad. Sci., Paris, 86 (1878), 589-592.
J10.178

ÇALLIALP F.,
[1] On the class number of real quadratic fields and the Riemann hypothesis (Turkish, English summary), Doga Math., 14 (1990), no. 2, 114-119.
M91h:11121

CAMERON D.,
[1] Euler and Maclaurin made easy, Math. Sci., 12 (1987), no. 1, 3-20.
Z649.41021; M89g:41021; R1988,1B4

CAMPBELL R.,
[1] Les intégrales eulériennes et leurs applications. Étude approfondie de la fonction gamma. Collection Universitaire de Mathématiques, XX. Dunod, Paris 1966 xxv+268 pp.
Z174.36201; M34#6161; R1967,9B132K

CANDELPERGHER B., COPPO M.A., DELABAERE E.,
[1] La sommation de Ramanujan, Enseign. Math. (2) 43 (1997), no. 1-2, 93-132.
Z884.40008; M99a:11149

CANTERZANI S.,
[1] Lettera a Torquato Vareno, sopra una maniera di cavare i numeri Bernoulliani, Mem. Mat. e Fis. Soc. Ital., Modena, 11, (1804), 173-180.

CAO ZHEN FU,
[1] On the Diophantine equation $x^4-py\sp 2=z\sp p$ C. R. Math. Rep. Acad. Sci. Canada 17 (1995), no. 2-3, 61-66. Corrig.: C. R. Math. Rep. Acad. Sci. Canada 18 (1996), no. 5, 233-234.
Z857.11011; M96h:11020, 97i:11026

CARDA K.,
[1] Zur Theorie der Bernoullischen Zahlen, Monatsh. Math. und Phys., 5 (1894), 185-192.
J25.412

[2] Darstellung der Bernoullischen Zahlen durch bestimmte Integrale, Monatsh. Math. und Phys., 5 (1894), 321-324.
J25.413

[3] Über eine Beziehung zwischen bestimmten Integralen, Monatsh. Math. und Phys., 6 (1895), 121-126.
J26.317

CARLITZ L.,
[1] An analogue of the von Staudt-Clausen theorem, Duke Math. J., 3 (1937), 503-517.
J63.II.879; Z17.195

[2] An analogue of the von Staudt-Clausen theorem, Duke Math. J., 7 (1940), 62-67.
J66,562; Z24.244; M2-146e

[3] An analogue of the Bernoulli polynomials, Duke Math. J., 8 (1941), 405-412.
Z25,96; M2-342e

[4] Generalized Bernoulli and Euler numbers, Duke Math. J., 8 (1941), 585-589.
Z63/I; M3-67b

[5] The coefficients of the reciprocal of a series, Duke Math. J., 8 (1941), no. 3, 689-700.
Z63/I; M3-147j

[6] q-Bernoulli numbers and polynomials, Duke Math. J., 15 (1948), 987-1000.
Z32,003; M10-283g

[7] Some properties of Hurwitz series, Duke Math. J., 16 (1949), no. 2, 285-295.
Z41,174; M10-593e

[8] Congruences for the coefficients of the Jacobi elliptic functions, Duke Math. J., 16 (1949), no. 2, 297-302.
Z38,179; M10-593f

[9] Congruences for the coefficients of hyperelliptic and related functions, Duke Math. J., 19 (1952), no. 2, 329-337.
Z48,30; M13-913j

[10] Note on irreducibility of the Bernoulli and Euler polynomials, Duke Math. J., 19 (1952), 475-481.
Z47,257; M14-163h

[11] Some theorems on Bernoulli numbers of higher order, Pacific J. Math., 2 (1952), 127-139.
Z46,40; M14-138d

[12] A divisibility property of the Bernoulli polynomials, Proc. Amer. Math. Soc. 3 (1952), 604-607.
Z49,163; M14-539d

[13] A note on Bernoulli numbers and polynomials of higher order, Proc. Amer. Math. Soc., 3 (1952), 608-613.
Z49,163; M14-539e

[14] Some congruences for the Bernoulli numbers, Amer. J. Math., 75 (1953), 163-172.
Z50,39; M14-539c; R1954,2861

[15] Some congruences of Vandiver, Amer. J. Math., 75 (1953), 707-712.
Z51,276; M15-201a; R1954,4340

[16] Some sums containing Bernoulli functions, Amer. Math. Monthly, 60 (1953), 475-476.
Z51,7; M15-104h; R1954,3209

[17] A theorem of Glaisher, Canad. J. Math., 5 (1953), 306-316.
Z52,38; M14-1064b; R1954,3216

[18] Note on the class number of real quadratic fields, Proc. Amer. Math. Soc., 4 (1953), 535-537.
M15-104g; R1954,3214

[19] Some sums connected with quadratic residues, Proc. Amer. Math. Soc., 4 (1953), 12-15.
Z50,267; M14-621e; R1953,565

[20] A note on Bernoulli and Euler numbers of order $\pm p$, Proc. Amer. Math. Soc., 4 (1953), 178-183.
Z51,276; M14-1064d; R1954,1051

[21] Remark on a formula for the Bernoulli numbers, Proc. Amer. Math. Soc., 4 (1953), 400-401.
Z50,9; M14-973h; R1954,2518

[22] A note on the multiplication formulas for the Bernoulli and Euler polynomials, Proc. Amer. Math. Soc., 4 (1953), 184-188.
Z51,250; M14-640h; R1953,1052

[23] A special congruence, Proc. Amer. Math. Soc., 4 (1953), 933-936.
Z52,38; M15-400h; R1955,55

[24] The class number of an imaginary quadratic field, Comm. Math. Helv., 27 (1953), 338-345.
Z52,34; M15-404d; R1955,2540

[25] Some theorems on Kummer's congruences, Duke Math. J., 20 (1953), 423-431.
Z51,276; M15-10f; R1954,3614

[26] The multiplication formulas for the Bernoulli and Euler polynomials, Math. Mag., 27 (1953), 59-64.
Z51,307; M15-308g; R1955,1813

[27] Some theorems on the Schur derivative, Pacific J. Math., 3 (1953), 321-332.
Z50,38; M14-951e; R1954,3217

[28] Some theorems on generalized Dedekind sums, Pacific J. Math., 3 (1953), 513-522.
Z57,37; M15-12b; R1954,3219

[29] Some congruences of Bernoulli numbers of higher order, Quarter. J. Math. Oxford Ser.(2), 4 (1953), 112-116.
Z50,267; M14-1064c; R1954,1976

[30] Note on a theorem of Glaisher, J. London Math. Soc., 28 (1953), 245-246.
Z50,267; M14-726b; R1953,566

[31] The first factor of the class number of a cyclic field, Canad. J. Math., 6 (1954), 23-26.
Z55,34; M15-686b; R1954,5046

[32] A theorem of Ljunggren and Jacobsthal on Bernoulli numbers, Proc. Amer. Math. Soc., 5 (1954), 34-37.
Z55,35; M15-507a; R1955,611

[33] Note on irregular primes, Proc. Amer. Math. Soc., 5 (1954), 329-331.
Z58,37; M15-778b; R1955,2090

[34] $q$-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc., 76 (1954), 332-350.
Z58,12; M15-686a; R1956,180

[35] Hankel determinants and Bernoulli numbers, Tôhoku Math. J. (2), 5 (1954), 272-276.
Z55,270; M15-777d; R1955,3052

[36] Note on the cyclotomic polynomial, Amer. Math. Monthly, 61 (1954), 106-108.
Z55,35; M15-508d; R1955,612

[37] A note on generalized Dedekind sums, Duke Math. J., 21 (1954), 399-403.
Z57,37; M16-14f; R1955,3603

[38] Dedekind sums and Lambert series, Proc. Amer. Math. Soc., 5 (1954), 580-584.
Z57,38; M16-14d; R1955,4853

[39] Extension of a theorem of Glaisher and some related results, Bull. Calcutta Math. Soc., 46 (1954), no. 2, 77-80.
Z56,268; M16-570b; R1955,4853

[40] A note on power residues, Duke Math. J., 22 (1955), no. 4, 583-587.
M17-713d; R1959,9743

[41] Note on the class number of quadratic fields, Duke Math. J., 22 (1955), 589-593.
Z66,27; M17-713e; R1959,9743

[42] A degenerate Staudt-Clausen theorem, Arch. Math. und Phys., 7 (1956), 28-33.
Z70,40; M17-586a; R1956,7091

[43] Arithmetic properties of elliptic functions, Math. Z., 64 (1956), no. 4, 425-432.
Z72,33; M17-1057e; R1958,8953

[44] A note on Bernoulli numbers of higher order, Scripta Math., 22 (1956), 217-221.
Z78,32; M19-941c; R1958,4477

[45] The coefficients of $\sinh x/ \sin x$, Math. Mag., 29 (1956), 193-197.
Z70,273; M17-944e; R1957,83

[46] A note on Kummer's congruences, Arch. Math., 7 (1957), 441-445.
Z77,51; M19-120a; R1957,8427

[47] A note on the Staudt-Clausen theorem, Amer. Math. Monthly, 64 (1957), 19-21.
Z77,51; M18-560c; R1957,7620

[48] Some polynomials of Touchard connected with the Bernoulli numbers, Canadian J. Math., 9 (1957), no. 2, 188-190.
Z77,281; M19-27e; R1959,534

[49] Expansion of q-Bernoulli numbers, Duke Math. J., 25 (1958), 355-364.
Z102,32; M20#2480; R1959,4425

[50] Bernoulli and Euler numbers and orthogonal polynomials, Duke Math. J., 26 (1959), 1-15.
Z85,287; M21#2761; R1960,1287

[51] Multiplication formulas for products of Bernoulli and Euler polynomials, Pacific J. Math., 9 (1959), no. 3, 661-666.
Z89,280; M21#7317; R1961,4B458

[52] Some congruences involving binomial coefficients, Elem. Math., 14 (1959), no. 1, 11-13.
Z85,28; M20#6384; R1959,9762

[53] Composition of sequences satisfying Kummer's congruences, Memoria publicada en Collectanea Mathematica (Barcelona), XI (1959), 137-152.
Z96,27; M22#4671; R1961,2A97

[54] Note on the coefficients of $\cosh x / \cos x$, Math. Mag., 32 (1959), 132-136.
Z95,262; M21#2754; R1960,1316

[55] Eulerian numbers and polynomials, Math. Mag., 32 (1959), no. 5, 247-260.
Z92,66; M21#3596; R1961,1B349

[56] Some finite summation formulas of arithmetic character, Publ. Math. Debrecen, 6 (1959), 262-268.
Z97,264; M22#1549; R1962,2A142

[57] A property of the Bernoulli numbers, Amer. Math. Monthly, 66 (1959), 714-715.
R1960,8581

[58] Arithmetic properties of generalized Bernoulli numbers, J. Reine Angew. Math., 202 (1959), 174-182.
Z125,22; M22#20; R1960,8580

[59] Some arithmetic properties of generalized Bernoulli numbers, Bull. Amer. Math. Soc., 65 (1959), 68-69.
Z82,32; M21#3383; R1960,6167

[60] Note on the integral of the product of several Bernoulli polynomials, J. London Math. Soc., 34 (1959), 361-363.
Z86,58; M21#5750; R1960,10534

[61] Kummer's congruences $\pmod{2^r}$, Monatsh. Math., 63 (1959), 394-400.
Z103,26; M21#6350; R1960,6145

[62] A special case of Kummer's congruences $\pmod{2^e}$, Enseigment Math. (2), 5 (1959), 171-175 (1960).
Z104,267; M23#A1587; R1960,12480

[63] Note on Nörlund's polynomial $B_n^{(z)}$, Proc. Amer. Math. Soc., 11 (1960), 452-455.
Z100,17; M22#5587; R1961,3B61

[64] Eulerian numbers and polynomials of higher order, Duke Math. J., 27 (1960), no. 3, 401-423.
Z104,290; M23#A1588; R1961,6A139

[65] Multiplication formulas for generalized Bernoulli and Euler polynomials, Duke Math. J., 27 (1960), no. 4, 537-545.
Z132,55; M22#9636; R1961,12B314

[66] A property of the Bernoulli numbers, Amer. Math. Monthly, 67 (1960), no. 10, 1011-1012.
R1961,9A148

[67] Kummer's congruences for the Bernoulli numbers, Portug. Math., 19 (1960), 203-210.
Z95,30; M23#A2361; R1961,9A153

[68] A note on Bernoulli and Euler polynomials of the second kind, Scripta Math., 25 (1961), no. 4, 323-330.
Z118,65; M25#4138; R1963,3B44

[69] Criteria for Kummer's congruences, Acta Arith., 6 (1961), 375-391.
Z99,28; M27#4786; R1952,3A104

[70] The Staudt-Clausen theorem, Math. Mag., 34 (1961), 131-146.
Z122,47; M24#A258; R1961,12A212

[71] A generalization of Maillet's determinant and a bound for the first factor of the class-number, Proc. Amer. Math. Soc., 12 (1961), 256-261.
Z131,36; M22#12093; R1962,1A139

[72] Some generalized multiplication formulas for the Bernoulli polynomials and related functions, Monatsh. Math., 66 (1962), no. 1, 1-8.
Z102,55; M25#2244; R1963,3B44

[73] A note on sums of powers of integers, Amer. Math. Monthly, 69 (1962), 290-291.

[74] A conjecture concerning the Euler numbers, Amer. Math. Monthly, 69 (1962), no.6, 538-540.
Z105,264; R1963,4B55

[75] A note on Eulerian numbers, Arch. Math., 14 (1963), 383-390.
Z116,251; M28#3960

[76] Some formulas for the Bernoulli and Euler polynomials, Math. Nachr., 25 (1963), 223-231.
Z112,45; M27#2663; R1964,1B53

[77] Generalized Dedekind sums, Math. Z., 85 (1964), no. 1, 83-90.
Z122,47; M29#3427; R1965,3A135

[78] Summation of certain series, Amer. Math. Monthly, 71 (1964), 41-44.
Z129,46; R1964,12B33

[79] Recurrences for the Bernoulli and Euler numbers, J. Reine Angew. Math., 214/215 (1964), 184-191.
Z126,262; M28#3961; R1965,3A136

[80] Extended Bernoulli and Eulerian numbers, Duke Math. J., 31 (1964), 667-689.
Z127,295; M29#5796; R1965,7B39

[81] Recurrences for the Bernoulli and Euler numbers II, Math. Nachr., 29 (1965), 151-160.
Z151,15; M31#5825; R1967,8V221

[82] The coefficients of $\cosh x/ \cos x$, Monatsh. Math., 69 (1965), 129-135.
Z141,41; M31#1222; R1965,11A151

[83] Linear relations among generalized Dedekind sums, J. Reine Angew. Math., 220 (1965), 154-162.
Z148,273; M32#88; R1966,10A79

[84] A theorem on generalized Dedekind sums, Acta Arith., 11 (1965), no. 2, 253-260.
Z131,288; M32#87; R1966,5A110

[85] The irreducibility of the Bernoulli polynomial $B_{14}(x)$, Math. Comp., 19 (1965), 667-670.
Z135,17; M33#117; R1966,9A128

[86] Some properties of the Nörlund polynomial $B_n^{(x)}$, Math. Nachr., 33 (1967), 297-311.
Z154,293; M36#129; R1967,12V280

[87] Bernoulli numbers, Fibonacci Quart., 6 (1968), no.3, 71-85.
Z159,56; M38#1071; R1970,6V335

[88] Some unusual congruences for the Bernoulli and Genocchi numbers, Duke Math. J., 35 (1968), 563-566.
Z169,368; M37#2672; R1969,6V225

[89] A conjecture concerning Genocchi numbers, K. Norske Vidensk. Selsk. Sk., (1971), No. 9, 1-4.
Z245.05004; M45#6749; R1972,4B73

[90] A note on Bernoulli numbers and polynomials, Elemente Math., 29 (1974), 90-92.
Z283.10003; M50#4604; R1975,2V454

[91] Note on some convolved power sums, SIAM J. Math. Anal., 8 (1977), no. 4, 701-709.
Z363.10008; M56#3384; R1978,2V417

[92] Generalized Stirling and related numbers, Revista Mat. Univ. Parma (4), 4 (1978), 79-99.
Z402.10017; M80h:10017; R1980,7V487

[93] A characterization of the Bernoulli and Euler polynomials, Rend. Sem. Mat. Univ. Padova, 62 (1980), 309-318.
Z443.33020; M81k:10020; R1981,8V590

[94] Some polynomials related to the Bernoulli and Euler polynomials, Util. Math., 19 (1981), 81-127.
Z474.10012; M82j:10023; R1981,12B38

[95] Some remarks on the multiplication theorems for the Bernoulli and Euler polynomials, Glas. Math. (3), 16 (36) (1981), no. 1, 3-23, (Serbo-Croatian Summary).
Z474.10013; M83b:10009; R1982,3B34

[96] The reciprocity theorem for Dedekind sums, Pacific J. Math., 3 (1953), 523-527.
R1954,2515

[97] A note on Euler numbers and polynomials, Nagoya Math. J., 7 (1954), 35-43.
R1956,179

[98] Note on a formula of Hermite, Math. Mag., 33 (1959/60), 7-11.
M21#5602; R1960,9983

[99] A recurrence formula for $\zeta(2n)$. Proc. Amer. Math. Soc., 12 (1961), no. 6, 991-992.
Z101,39; M24#A3140; R1962,7B42

[100] Some arithmetic properties of a special sequence of integers, Canad. Math. Bull., 19 (1976), no. 4, 425-429.
M56#239

[101] Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51-88.
Z404.05004; M80i:05014; R1979,11V408

[102] Explicit formulas for the Dumont-Foata polynomials, Discrete Math., 30 (1980), no. 3, 211-225.
M81f:05007; R1980,10V450

[103] Some restricted multiple sums, Fibonacci Quart. 18 (1980), no. 1, 58-65.
Z426.10014; M84c:05012; R1980,9A119

[104] Some arithmetic properties of the Olivier functions, Math. Ann., 128 (1955), 412-419.
Z065.27203; M16,677b; R1956,181

[105] Generating functions, Fibonacci Quart. 7 (1969), no. 4, 359-393.
Z194.00701; M41 #8254; R1970,10V210

CARLITZ L., LEVINE J.,
[1] Some problems concerning Kummer's congruences for the Euler numbers and polynomials, Trans. Amer. Math. Soc., 96 (1960), 23-37.
Z99,29; M22#6768; R1961,5A150

CARLITZ L., OLSON F.R.,
[1] Some theorems on Bernoulli and Euler numbers of higher order, Duke Math. J., 21 (1954), 405-421.
Z56,36; M15-934b; R1955,4216

CARLITZ L., RIORDAN J.,
[1] Congruences for Eulerian numbers, Duke Math. J., 20 (1953), no. 3, 339-343.
Z51,276; M15-10e; R1954,4341

[2] The divided central difference of zero, Canad. J. Math., 15 (1963), 94-100.
Z108,251; M26#48

CARLITZ L., SCOVILLE R.,
[1] The sign of the Bernoulli and Euler numbers, Amer. Math. Monthly, 80 (1973), 548-549.
Z273.10012; M47#4917

[2] Tangent numbers and operators, Duke Math. J., 39 (1972), 413-429.
Z243.05009; M46#1968; R1973,5V422

[3] Enumeration of up-down permutations by upper records, Monatsh. Math., 79 (1975), 3-12.
Z315.05004; M50#12748; R1975,10V259

[4] Enumeration of rises and falls by position, Discrete Math., 5 (1973), 45-59.
Z259.05008; M47#1626; R1973,11B434

[5] Generating functions for certain types of permutations, J. Combinatorial Theory Ser. A, 18 (1975), no. 3, 262-275.
Z303.05007; M51#7890; R1975,11B334

CARLITZ L., STEVENS H.,
[1] Criteria for generalized Kummer's congruences, J. Reine Angew. Math., 207 (1961), 203-220.
Z99,29; M23#A1585; R1962,3A105

CARLITZ L.: see also AL-SALAM W.A., CARLITZ L.

CARMICHAEL R.D.,
[1] The theory of numbers and diophantine analysis, New York, 1915.
J42.283

CARR G.S.,
[1] A synopsis of elementary results in pure mathematics containing propositions, formulae, and methods of analysis, with abridged demonstrations. Macmillan and Bowes, Cambridge, 1886. xxxvi + 936 pp.
J17.1154

CARTIER P.,
[1] An introduction to zeta functions. From number theory to physics (Les Houches, 1989), 1-63. Springer, Berlin, 1992.
Z790.11061; M94b:11081

CARTIER P., ROY Y.,
[1] Certains calculs numériques relatifs à l'interpolation p-adique des séries de Dirichlet. In: Modular functions of one variable III, pp. 269-349. Lecture Notes in Math., Vol. 350, Springer-Verlag, Berlin, 1973.
Z265.10021; M48#8451; R1974,6A447

CASSELS J.W.S.,
[1] Local Fields. London Math. Soc. Student Texts, 3. Cambridge Univ. Press, Cambridge-New York, 1986. xiv + 360 pp.
Z595.12006; M87i:11172; R1987,8A307

CASSOU-NOGUÈS PH., TAYLOR M.J.,
[1] Un élément de Stickelberger quadratique, J. Number Theory, 37 (1991), no. 3, 307-342.
Z719.11075; M92e:11125

CASSOU-NOGUÈS P.,
[1] Formes linéaires p-adiques et prolongement analytique. Sémin. Théor. Nombres, 1970-71 (Univ. Bordeaux I, Talence), Exp. No. 14, 7 pp., Talence, 1971.
Z227.12005; M53#2904

[2] Formes linéaires p-adiques et prolongement analytique, C.R. Acad. Sci. Paris, A 274 (1972), 5-8.
Z227.12005; M45#5092; R1972,6A348

[3] Formes linéaires p-adiques et prolongement analytique, Bull. Soc. Math. France, (1974), Suppl., no. 39/40, 23-26.
Z301.12004; M50#12985; R1975,7A475

[4] Analogues p-adiques de certaines fonctions arithmétiques. Sémin. Théor. Nombres, 1974-75 (Univ. Bordeaux I, Talence), Exp. No. 24, 12 pp., Talence, 1975.
Z386.12011; M53#363; R1976,7A434

[5] Prolongement analytique et valeurs aux entiers négatifs de certaines séries arithmétiques relatives à des formes quadratiques. Sémin. Théor. Nombres, 1975-76 (Univ. Bordeaux I, Talence), Exp. No. 4, 34 pp., Talence, 1976.
Z227.12005; M55#12696

[6] Valeurs aux entiers négatifs des fonctions zêta et des fonctions zêta p-adiques, Invent. Math., 51 (1979), no. 1, 29-59.
Z408.12015; M80h:12009b; R1979,9A328

[7] Séries de Dirichlet. Séminaire de théorie des nombres. Univ. Bordeaux I, Année 1980-81, Exposé no. 22, 14 pp. (1981).
Z507.12007; M84b:12017

[8] Applications arithmétiques de l'étude des valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme, Ann. Inst. Fourier, 31 (1981), Suppl., fasc. 4, 1-36.
Z496.12009; M83e:12011; R1982,6A114

[9] Valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme, 1, J. Number Theory, 14 (1982), no. 1, 32-64.
Z496.12008; M83e:12012; R1982,8A359

CASTELLANOS D.,
[1] The ubiquitous $\pi$. I. Math. Mag., 61 (1988), no. 2, 67-98.
Z654.10001; M89c:01025; R1989,3A7

[2] The ubiquitous $\pi$. II. Math. Mag., 61 (1988), no. 3, 148-163.
M89c:11184

[3] A generalization of Binet's formula and some of its consequences. Fibonacci Quart., 27 (1989), no. 5, 424-438.
Z689.10020, 723.11006; M91e:11018

[4] A note on Bernoulli polynomials, Fibonacci Quart., 29 (1991), no. 2, 98-102.
Z725.11010; M92h:11018

CATALAN E.,
[1] Sur les différences de $1^p$ et sur le calcul des nombres de Bernoulli, Annali sci. mat. e fis., Roma, 2 (1859), 195-199, Annali di Matematica Pura et Applicata, (1) 2 (1859), 239-243.

[2] Sur les nombres de Bernoulli et sur quelques formules qui en dépendent, C.R. Acad. Sci. Paris, 54 (1862), 1030-1033, 1059-1062.

[3] Remarques sur une note de M. Le Besgue (relative aux nombres de Bernoulli), C.R. Acad. Sci. Paris, 58 (1864), 902-904.

[4] Sur les calcul des nombres de Bernoulli, C.R. Acad. Sci. Paris, 58 (1864), 1105-1108.

[5] Sur les nombres d'Euler, C.R. Acad. Sci. Paris, 66 (1868), 415-416.

[6] Sur les nombres de Bernoulli et d'Euler et sur quelques intégrales définies, Brux. Acad. Sci. Mém., 37 (1869), 1-19.
J2.155

[7] Recherches sur le développement de la fonction $\Gamma$, Bull. de l'Acad., Bruxelles, 36 (1873), 4-16.
J5.169

[8] Note sur les nombres de Bernoulli, Bull. de l'Acad., Bruxelles, 81 (1875), 441-443.
J7.160

[9] Rapport sur la note de Mr. Le Paige, Bull. Acad. Royal Sci. Belgiques (2), 61 (1876), 935-939.

[10] Note sur la communication de précédente, Bull. Acad. Royal Sci., Belgiques (2), 41 (1876), 1018-1019.
J8.147

[11] Extrait d'une lettre de M. Catalan à M. G. de Longchamps (Sur les nombres de Bernoulli), Nouv. Corres. Math., 4 (1878), 119.
J8.193

[12] Sur les manières contradictoires de définir les nombres de Bernoulli, Nouv. Corres. Math., 5 (1879), 196-198.

[13] Extraits d'une lettre à M. Hermite, Nouv. Corres. Math., 6 (1880), 320-321.
J12.122

[14] Théorème de Staudt et de Clausen, Bull. Sci. Math. et Astr. (2), 4 (1880), 77-82.
J12.128

[15] Mélanges mathématiques, Mém. Soc. Royal. Sci., Liège (2), 12 (1885), 1-407.
J17.22

[16] Mémoires de la Sociétée Royale des Sciences, XII (1885), Chapters: XXXII, XXXIII, XXXIV, XXXV, LXXVI, 86-119, 320-327.

CATALAN E.: see also LUCAS E., CATALAN E.

CATTABIANCHI L.T.,
[1] Numeri e polinomi di Bernoulli parametrizzati, Riv. Mat. Univ. Parma (2), 4 (1963), 281-291.
Z149,44; M32#1378

CAUCHY A.L.,
[1] Sur la théorie des nombres, Bull. Sci. Math., Phys. et Chim., Paris, 15 (1831), 137-139.

[2] Mémoire sur la théorie des nombres, Mémoires Acad. Sci., Paris, 17 (1840), 249-269, 435-455.

CAYLEY A.,
[1] A dissertation on Bernoulli's numbers, Messeng. Math., 4 (1875), 157-160.
J7.132

CELÉRIER C.,
[1] Démonstration d'un théorème fondamental relatif aux facteurs primitifs des nombres premiers, Applications au théorème de Fermat et à la recherche des facteurs primitifs, Mém. Soc. de Phys. et d'Hist. Nat. de Genève, 32 (1896), partie 2, no. 7, 1-61.
J28.188

CELKO M.,
[1] On the sums of some infinite series using the Bernoulli numbers (Slovak). In: Kovácik, O. (Ed.), Proceedings of the seminar on orthogonal polynomials and other applications, held in Zilina, Slovakia. Univ. of Transport and Communications, Dept. of Math., Zilina, 1993. pp. 3-6.
Z793.40002

CESÀRO E.,
[1] Quelques formules, Nouv. Corres. Math., 6 (1880), 450-452.

[2] Principes du calcul symbolique, Mathesis, 3 (1883), 10-17.
J15.206

[3] Sull' inversione delle indentità arithmetiche, Giorn. Mat., 23 (1885), 168-174.
J17.138

[4] Sur les nombres de Bernoulli et d'Euler, Nouv. Ann. Math. (3), 5 (1886), 305-327, 496.
J18.227

[5] Sur un théorème de M. Lipschitz, et sur la partie fractionnaire des nombres de Bernoulli, Annali Mat., Milano (2), 14 (1886), 221-226.
J18.226

[6] Sur les démonstrations du théorème de Staudt et de Clausen, Bull. Acad. Royale Sci. Belgique (3), 20 (1890), 280-289.
J22.267

[7] A proposito d'una generalizzazione della funzione $\varphi$ de Gauss, Periodico de Mat., 7 (1892), 1-6.
J24.167

[8] Elementares Lehrbuch der algebraischen Analysis und der Infinitesimalrechnung mit zahlreichen Übungsbeispielen. Nach einem Manuskript des Verfassers deutsch herausgegeben von G. Kowalewski, Leipzig, 1904.
J35.294

CHABA A.N.: see BEZERRA V.B., CHABA A.N.

CHANG KU-YOUNG, KWON SOUN-HI,
[1] Class number problem for imaginary cyclic number fields, J. Number Theory 73 (1998), no. 2, 318-338.

CHARALAMBIDES CH.A.,
[1] Bernoulli related polynomials and numbers, Math. Comp., 33 (1979), no. 146, 794-804.
Z402.10009; M80h:10018; R1980,2V594

CHARKANI EL HASSANI M.,
[1] Involution de Leopoldt et unités elliptiques. Thèse doct. 3ème cycle, math. pure, Univ. Sci. et Méd. Grenoble, 1984, 47 pp.
R1987,5A310D

CHARKANI EL HASSANI M., GILLARD R.,
[1] Unités elliptiques et groupes de classes, Ann. Inst. Fourier, 36 (1986), no. 3, 29-41.
Z597.12005; M88f:11056; R1987,5A311

CHEBYSHEV P.L.,
[1] Note sur différentes séries, J. de Math. (1), 16 (1851), 337-346.

CHELLALI M.,
[1] Nombres de Bernoulli modulo $p^m$ et nombres premiers irréguliers, Thèse Doct. 3ème cycle, math. pure, Univ. Sci. et Méd. Grenoble, (1982), Var. pag.
R1986,9A652

[2] Accélération de calcul de nombres de Bernoulli, J. Number Theory, 28 (1988), no. 3, 347-362.
Z644.10010; M89h:05002; R1988,10A112

[3] Congruences entre nombres de Bernoulli-Hurwitz dans le cas supersingulier, J. Number Theory, 35 (1990), no. 2, 157-179.
Z705.11008; M92f:11079

CHEN JING RUN, LI JIAN YU,
[1] On the sums of powers of natural numbers, Chinese Quart. J. Math., 2 (1987), no. 1, 1-17.
Z636.10008; M90i:11108

CHEN KWANG-WU: see EIE M., CHEN KWANG-WU

CHEN MING-PO, SRIVASTAVA H.M.,
[1] Some families of series representations for the Riemann $\zeta(3)$, Result. Math., 33 (1998), no.3-4, 179-197.
Z980.45948

CHEN TIAN PING,
[1] Asymptotic expansions for splines, Approx. Theory Appl., 2 (1986), no.2, 1-9.
Z608.41006; M88e:41026

CHEN XUMING,
[1] Recursive formulas for $\zeta(2k)$ and $L(2k-1)$, College Math. J., 26 (1995), no. 5, 372-376.

CHEN ZHI MING,
[1] Some identities for Euler numbers and Bernoulli numbers (Chinese), Pure Appl. Math., 10 (1994), no. 1, 7-10.
Z841.11009; M95h:11015

CHILDRESS N., GOLD R.,
[1] Zeros of p-adic L-functions, Acta Arith., 48 (1987), no. 1, 63-71.
Z565.12009; M88i:11091; R1987,12A272

CHISTYAKOV I.I.,
[1] Bernullievy chisla [Bernoulli numbers]. Moscow, 1895.
J26,283

CHOI JUNESANG,
[1] Explicit formulas for Bernoulli polynomials of order $n$, Indian J. Pure Appl. Math., 27 (1996), no. 7, 667-674.
Z860.11009; M97e:11029

CHOLEWINSKI F.M.,
[1] The Finite Calculus Associated With Bessel Functions. Contemporary Mathematics, Vol. 75. Amer. Math. Soc., Providence, R.I., 1988.
Z691.05007; M89m:05013

CHOWLA P., CHOWLA S.,
[1] A note on Bernoulli numbers, J. Number Theory, 12 (1980), 445-446.
Z445.10014; M82c:10013; R1981,6A327

[2] On Bernoulli numbers, II, J. Number Theory, 14 (1982), no. 1, 65-66.
Z485.10010; M82m:10022; R1982,7A101

[3] Criterion for the class number of some real quadratic fields to be 1, Norske Vid. Selsk. Skr. (Trondheim), 1986, no. 2, 1.
Z617.12002; R1987,12A288

[4] Criteria for the class number of quadratic fields to be 1, Norske Vid. Selsk.Skr. (Trondheim), 1986, no. 2, 2-3.
Z617.12003; R1987,12A289

[5] Some unsolved problems, Norske Vid. Selsk. Skr. (Trondheim), 1986, no. 2, 7.
Z617.12008; R1987,12A290

CHOWLA S.,
[1] A new proof of Von Staudt's theorem, J. Indian Math. Soc., 16 (1926), 145-146.
J62.140

[2] Some properties of Eulerian and prepared Bernoullian numbers, Messenger Math., 57 (1927), 121-126.
J54.182

[3] On a conjecture of Ramanujan, Tôhoku Math. J., 33 (1930), 1-2.
J56.II.875

[4] A note on Bernoulli's numbers. In: Proc. Number Theory, Conf. at Calif. Inst. of Tech., Summer, 1955.

[5] On the signs of certain generalized Bernoulli numbers, Kgl. Norske Vid. Selskabs Forhandl., (1961), 34 (1962), no. 21, 102-104.
Z105,25; M25#2043; R1962,10A96

[6] Leopoldt's criterion for real quadratic fields with class-number 1, Abhandl. Math. Sem. Univ. Hamburg, 35 (1970), 32.
Z222.12002; M43#3232; R1971,5A373

[7] On some formulae resembling the Euler-Maclaurin sum formula, Kgl. Norske Vid. Selskabs Forhandl., 34 (1961/62), no.23, 107-109.
M25#2044; R1962,10A94

CHOWLA S., HARTUNG P.,
[1] An "exact" formula for the m-th Bernoulli number, Acta. Arith., 22 (1972), 113-115.
Z244.10008; M46#7151; R1973,3V334

CHOWLA S.: see also ANKENY N.C., ARTIN E., CHOWLA S.

CHOWLA S.: see also ANKENY N.C., CHOWLA S.

CHOWLA S.: see also CHOWLA P., CHOWLA S.

CHU W.: see HSU L.C., CHU W.

CHU WEI PAN: see DANG SI SHAN, CHU WEI PAN

CIBRARIO M.,
[1] Sui numeri di Bernoulli e di Eulero, Rendic. Accad. d. Lincei, Cl. Sci., Roma (6), 18 (1933), 110-118.
J59.I.171; Z7,413

[2] Sui polinomii di Bernoulli e di Eulero, Rendiconti Accad. d. L. Roma (6), 18 (1933), 207-214.
J59.II.1050; Z8.162

[3] Su alcune generalizzazioni dei numeri e dei polinomii de Bernoulli e di Eulero, Rendiconti Accad. d. L. Roma (6), 18 (1933), 275-279.
Z8.162

[4] Proprietà dei numeri e dei polinomii di Bernoulli e di Eulero generalizzati, Rendiconti Accad. d. L. Roma (6), 18 (1933), 365-369.
J59.II.1050; Z8.261

CIKÁNEK P.,
[1] Matrices of the Stickelberger ideals $\pmod l$ for all primes up to 125000, Arch. Math. (Brno), 27a (1991), 3-6.
Z760.11028; M93i:11149; R1992,10A239

[2] A special extension of Wieferich's criterion. Math. Comp., 62 (1994), no. 206, 923-930.
Z805.11027; M94g:11023

CLARKE F.,
[1] The universal von Staudt theorems, Trans. Amer. Math. Soc., 315 (1989), no. 2, 591-603.
Z683.10013; M90a:11026; R1990,9A97

[2] On Dibag's generalization of von Staudt's theorem, J. Algebra, 141 (1991), no. 2, 420-421.
Z734.11019; M92k:11020

[3] On Vandiver's generalised Bernoulli numbers, Preprint, 1990.

CLARKE F., SLAVUTSKII I.SH.,
[1] The integrality of the values of Bernoulli polynomials and of generalised Bernoulli numbers. Bull. London Math. Soc. 29 (1997), no. 1, 22-24.
Z865.11021; M97k:11022

CLARKE F.: see also BAKER A.J., CLARKE F., et al.

CLAUSEN T.,
[1] Lehrsatz aus einer Abhandlung über die Bernoullischen Zahlen, Astr. Nachr., 17 (1840), 351-352.

COATES J.,
[1] p-adic L-functions and Iwasawa's theory, Algebraic Number Fields, ed. Fröhlich A., London, 1977, 269-353.
Z393.12027; M57#276; R1979,5A288

[2] The work of Mazur and Wiles on cyclotomic fields, Lect. Notes in Math., 901 (1981), 220-242.
Z506.12001; M83i:12005; R1982,8A362

COATES J., POITOU G.,
[1] Du nouveau sur les racines de l'unité, Gaz. Math., 15 (1980), 5-26.
Z476.12007

COATES J., SINNOTT W.,
[1] On p-adic L-functions over real quadratic fields, Invent. Math., 25 (1974), no. 3/4, 253-279.
Z305.12008; M50#7093; R1975,2A401

COEN L.E.S.,
[1] Sums of Powers and the Bernoulli Numbers. M.A. thesis, Eastern Illinois University, Charleston, Illinois, 1996. 54pp.

COHEN H., OLIVIER M.,
[1] Calcul des valeurs de la fonction zêta de Riemann en multiprécision. C. R. Acad. Sci. Paris Ser. I Math., 314 (1992), no. 6, 427-430.
Z751.11057; M93g:11134

COHEN S.P.,
[1] Heights of torsion points on commutative group varieties, Proc London Math. Soc. (3), 52 (1986), no. 3, 427-444.
Z585.14032; M87i:14038; R1987,6A469

COHN H.,
[1] Introduction to the construction of class fields. Cambridge Studies in Advanced Math., 6. Cambridge Univ. Press, Cambridge-New York, 1985. x + 213 pp.
Z571.12001; M87i:11165; R1986,11A423

COLEMAN R.,
[1] Local units modulo circular units, Proc. Amer. Math. Soc., 89 (1983), no. 1, 1-7.
Z528.12005; M85b:11088; R1984,4A367

COMRIE L.J.: see FLETCHER A. et al.

COMTET L.,
[1] Analyse combinatoire. Tomes I, II. Presses Universitaires de France, Paris, 1970. 192 pp., 190 pp.
Z221.05001-2; M41#6697

[2] Advanced combinatorics. The art of finite and infinite expansions. Revised and enlarged edition. D. Reidel Publ. Co., Dordrecht-Boston, 1974. x + 343 pp.
Z283.05001; M57#124

CONWAY J.H., SLOANE N.J.A.,
[1] On enumeration of lattices of determinant one, J. Number Theory, 15 (1982), no. 1, 83-94.
Z496.10023; M84b:10047; R1982,12V585

COPPO M.A.: see CANDELPERGHER B., COPPO M.A., DELABAE RE E.,

CORNELISSEN G.,
[1] Zeros of Eisenstein series, quadratic class numbers and supersingularity for rational function fields, Math. Ann. 314 (1999), no. 1, 175-196.

COSTA PEREIRA N.: see PEREIRA N.C.

COSTABILE F.,
[1] Expansions of real functions in Bernoulli polynomials and applications. Conf. Semin. Mat. Univ. Bari No. 273, (1999), 13 pp.

COTLAR M.,
[1] Estudio de una classe de polinomios de Bernoulli, Math. Notae (Boletin Inst. Math.), Rosario, Argentina, 7 (1946), no. 2, 69-95.
Z61,140; M9-30f

[2] Un método para obtener congruencias de numeros de Bernoulli [A method for obtaining congruences of Bernoulli numbers], Math. Notae (Boletin Inst. Math.), Rosario, Argentina, 7 (1947), no. 1, 1-29.
Z30,014; M9-175c

COX D.A.,
[1] Introduction to Fermat's Last Theorem. Amer. Math. Monthly, 101 (1994), no. 1, 3-14.
Z849.11002; M94i:11022; R1994,10A246

CRANDALL R.E.,
[1] Topics in Advanced Scientific Computation. TELOS/Springer-Verlag, Santa Clara, CA, 1996.
M97g:65005

CRANDALL R.E., BUHLER J.P.,
[1] On the evaluation of Euler sums. Experiment. Math., 3 (1994), no. 4, 275-285.
Z833.11045; M96e:11113

CRANDALL R.E., DILCHER K., POMERANCE C.,
[1] A search for Wieferich and Wilson primes, Math. Comp., 66 (1997), no. 217, 433-449.
Z854.11002; M97c:11004; R1997,10A129

CRANDALL R.E.: see also BUHLER J.P. et al.

CRANDALL R.E.: see also BAILEY D.H., BORWEIN J.M., CRANDALL R.E.

CROMBEZ G.,
[1] On a generalization of the Bernoulli and Euler polynomials, Ganita, 22 (1971), no. 1, 131-141.
Z222.30019; M45#3810

CSORBA G.,
[1] Über die Partitionen der ganzen Zahlen, Math. Ann., 75 (1914), 545-568.
J45.285

CVIJOVIC D., KLINOWSKI J.,
[1] New formulae for the Bernoulli and Euler polynomials at rational arguments, Proc. Amer. Math. Soc., 123 (1995), no. 5, 1527-1535.
Z827.11012; M95g:11085

[2] New rapidly convergent series representations for $\zeta(2n+1)$, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1263-1271.
Z863.11055; M97g:11090

[3] Values of the Legendre chi and Hurwitz zeta functions at rational arguments. Math. Comp. 68 (1999), no. 228, 1623-1630.


DABROWSKI A.,
[1] A note on $p$-adic $q$-$\zeta$-functions, J. Number Theory 64 (1997), no. 1, 100-103.
Z876.11055; M98c:11128

DAMAMME G.,
[1] Transcendence properties of Carlitz zeta-values. The Arithmetic of Function Fields (Proceedings, Ohio State Univ., 1991), 303-311. Walter deGruyter, Berlin - New York 1992.
Z788.11021; M94a:11109

DANG SI SHAN, CHU WEI PAN,
[1] Some identities involving Euler numbers, Bernoulli numbers, and eneralized Stirling numbers of the first kind. (Chinese), Pure Appl. Math. 13 (1997), no. 2, 109-113, 117.
Z899.11007; M99d:11018

D'ANIELLO C.,
[1] On some inequalities for the Bernoulli numbers, Rend. Circ. Mat. Palermo (2), 43 (1994), no. 3, 329-332.
Z830.11108; M96f:11030

DARBOUX G.,
[1] Sur les développements en série des fonctions d'une seule variable, J. Math. Pures Appl. (3), 2 (1876), 291-312.
J8.124

DARMON H.: see BALOG A., DARMON H., ONO K.

DAVID E.,
[1] Applications de la dérivation d'Arbogast à la solution de la partition des nombres et à d'autres problèmes, J. Math. Pures Appl., 8, (1882), 61-72.
J14.129

DAVIS B.: see SITARAMACHANDRA RAO R., DAVIS B.

DAVIS H.T.,
[1] Tables of the Higher Mathematical Functions, v.2, Bloomington, Indiana: Principia Press, 1935, xiii + 391pp.
Z13,216

DEEBA E.Y., RODRIGUEZ D.M.,
[1] Stirling's series and Bernoulli numbers, Amer. Math. Monthly, 98 (1991), no.5, 423-426.
Z743.11012; M92g:11025; R1992,453

DELABAERE E.: see CANDELPERGHER B., COPPO M.A., DELABAERE E.,

DELANGE H.,
[1] Sur les zéros réels des polynômes de Bernoulli, C.R. Acad. Sci. Paris, 303, Série I, (1986), no. 12, 539-542.
Z607.10006; M88a:11020; R1987,3B31

[2] Sur les zéros imaginaires des polynômes de Bernoulli, C.R. Acad.Sci. Paris, 304, Série I, (1987), no. 6, 147-150.
Z607.10007; M88d:30009; R1987,7B20

[3] On the real roots of Euler polynomials, Monatsh. Math., 106 (1988), no. 2, 115-138.
Z653.10010; M89k:11009; R1989,3A250

[4] Sur les zéros réels des polynômes de Bernoulli, Ann. Inst. Fourier, Grenoble, 41 (1991), no. 2, 267-309.
Z739.11006 (725.11011); M93h:11023; R1992,6B16

DELIGNE P., RIBET K.A.,
[1] Values of Abelian L-functions at negative integers over totally real fields, Invent. Math., 59 (1980), no. 3, 227-286.
Z434.12009; M81m:12019; R1982,3A341

DELVOS F.J.,
[1] Bernoulli functions and periodic B-splines, Computing, 38 (1987), no. 1, 23-31.
Z616.65147; M88f:41017; R1987,11B1272

DEMAILLY J.P.,
[1] Sur le calcul numérique de la constante d'Euler, Gaz. Math., no. 27 (1985), 113-126.
M86m:11105

DE MOIVRE A.,
[1] Miscellanea analytica de seriebus et quadraturis, London, 1730.

DE MORGAN A.,
[1] Differential and Integral Calculus, Chapters XIII and XX, 1842.

DENCE J.B.,
[1] A development of Euler numbers, Missouri J. Math. Sci. 9 (1997), no. 3, 148-155.
M98h:11023

DENCE J.B., DENCE Th. P.,
[1] Elements of the theory of numbers. Harcourt/Academic Press, San Diego, CA, 1999. xviii+517 pp. ISBN 0-12-209130-2
M99k:11001

DÉNES P.,
[1] An extension of Legendre's criterion in connection with the first case of Fermat's last theorem, Publ. Math. Debrecen, 2 (1951), 115-120.
Z43,273; M13-822h

[2] Über die Diophantische Gleichung $x^{np + y^{np} = p^mz^{np}$, Czechoslovak Math. J. 1, 76 (1951) (1952), 179-185.
Z48,29; M16-903g

[3] Beweis einer Vandiver'schen Vermutung bezüglich des zweiten Falles des letzten Fermat'schen Satzes, Acta Sci. Math. (Szeged), 14 (1952), 197-202.
Z49,310; M14-451e

[4] Über die Diophantische Gleichung $x^l+y^l = cz^l$, Acta Math., 88 (1952), 241-251.
Z48,275; M16-903h

[5] Über irreguläre Kreiskörper, Publ. Math. Debrecen, 3 (1953) (1954), 17-23.
Z56,33; M15-686d; R1955,3043

[6] Über Grundeinheitssysteme der irregulären Kreiskörper von besonderen Kongruenzeigenschaften, Publ. Math. Debrecen, 3 (1954) (1955), 195-204.
Z58,269; M17-131c; R1957,69

[7] Über den zweiten Faktor der Klassenzahl und den Irregularitätsgrad der irregulären Kreiskörper, Publ. Math. Debrecen, 4 (1956), 163-170.
Z71,265; M18-20e; R1959,4421

DENINGER CH.,
[1] On the analogue of the formula of Chowla and Selberg for real quadratic fields, J. Reine Angew. Math., 351 (1984), 171-191.
Z527.12009; M86f:11085; R1985,1A215

DENNLER G.,
[1] Bestimmung sämtlicher meromorpher Lösungen der Funktionalgleichung $f(z) = {1 \over k} \sum_{h=0}^{k-1}{f({z+h \over k})}$, Wiss. Z. Friedrich-Schiller-Univ. Jena, Math.-Natur., 14 (1965), no. 5, 347-350.
Z146,132; M37#5559; R1968,1B202

DE PESLOUAN L.,
[1] Sur une congruence entre les nombres de Bernoulli, C. R. Acad. Sci. Paris, 170 (1920), 267-269.
J47.131

DEPINE R.A.: see BANUELOS A., DEPINE R.A.

DERR L.: see OUTLAW C., SARAFYAN D., DERR L.

DESBROW D.,
[1] Sums of integer powers, Math. Gaz., 66 (1982), no. 436, 97-100.
M83j:10054

DESNOUX P.-J.,
[1] Congruences dyadiques entre nombres de classes de corps quadratiques, Manuscr. Math., 62 (1988), no. 2, 163-179.
Z664.12002; M90c:11079; R1989,4A265

DE TEMPLE D. W., WANG SHUN HWA,
[1] Half-integer approximations for the partial sums of the harmonic series, J. Math. Anal. Appl., 160 (1991), no. 1, 149-158.
Z747.40002; M92j:41042

DEVANATHAN V.: see SUBRAMANIAN P.R., DEVANATHAN V.

DIAMOND J.,
[1] The $p$-adic log gamma function and $p$-adic Euler constants, Trans. Amer. Math. Soc. 233 (1977), 321-337.
Z382.12008; M58 #16610

[2] The p-adic gamma measures, Proc. Amer. Math. Soc., 75 (1979), no. 2, 211-218.
Z421.12019; M80d:12013; R1980,1A369

[3] On the values of p-adic L-functions at positive integers, Acta Arith., 35 (1979), no. 3, 223-237.
Z463.12007; M80j:12013; R1980,5A313

DIBAG I.,
[1] An analogue of the von Staudt-Clausen theorem, J. Algebra, 87 (1984), Suppl., no. 2, 332-341.
Z463.12007; M85j:11028; R1984,10A308

[2] Generalisation of the von Staudt-Clausen theorem, J. Algebra, 125 (1989), no. 2, 519-523.
Z683.10014; M90g:11025; R1990,5A275

DI CAVE A., RICCI P.E.,
[1] Sui polinomi di Bell ed i numeri di Fibonacci e di Bernoulli, Matematiche, 35 (1980), no. 1-2, 84-95.
Z534.33008; M84h:05011

DICKEY L.J., KAIRIES H.H., SHANK H.S.,
[1] Analogs of Bernoulli polynomials in fields $ Z_p$, Aequationes Math., 14 (1976), no. 3, 401-440.
Z343.12006; M53#13103; R1977,2A117

DICKSON J.D.H.: see BARNIVILLE J.J., DICKSON J.D.H., LAMPE E.

DICKSON L.E.,
[1] Notes on the theory of numbers, Amer. Math. Monthly, 18 (1911), 109-111.

[2] History of the Theory of Numbers, Washington, (1919-1923), vol. 1-3. Reprint: Chelsea Publ. Co., New York, 1966.
J47,100; 49,100; M39#6807a,b,c

DI CRESCENZO A., ROTA G.-C.,
[1] On umbral calculus (Italian. English summary), Ricerche Mat., 43 (1994), no. 1, 129-162.
M96e:05016

DIENGER J.,
[1] Die Lagrangesche Formel und die Reihensummierung durch dieselbe, J. Reine Angew. Math., 34 (1847), 75-100.

DIETER U.,
[1] Reciprocity theorems for Dedekind sums, IX. Mathematikertreffen Zagreb-Graz (Motovun, 1995), 11-24, Grazer Math. Ber., 328, Karl-Franzens-Univ. Graz, Graz, 1996.
Z880.11041; M98i:11024

DILCHER K.,
[1] Zero-free regions for Bernoulli polynomials, C.R. Math. Rep. Acad. Sci. Canada, 5 (1983), no. 6, 241-246.
Z532.30005; M85a:30015; R1984,3B30

[2] Irreducibility and zeros of generalized Bernoulli polynomials, C.R. Math. Rep. Acad. Sci. Canada, 6 (1984), no. 5, 273-278.
Z558.10012; M85k:11010; R1985,7A148

[3] On a Diophantine equation involving quadratic characters, Compositio Math., 57 (1986), no. 3, 383-403.
Z584.10008; M87e:11046; R1986,8A99

[4] Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters, J. Number Theory, 25 (1987), no. 1, 72-80.
M88a:11021; R1987,6A98

[5] Asymptotic behaviour of Bernoulli, Euler and generalized Bernoulli polynomials, J. Approx. Theory, 49 (1987), no. 4, 321-330.
Z609.10008; M88g:33001; R1987,10A63

[6] Zeros of Bernoulli, generalized Bernoulli and Euler polynomials, Mem. Amer. Math. Soc., 73 (1988), no. 386, iv + 94 pp.
Z645.10015; M89h:30005; R1988,10B22

[7] Multiplikationstheoreme für die Bernoullischen Polynome und explizite Darstellungen der Bernoullischen Zahlen, Abh. Math. Sem. Univ. Hamburg, 59 (1989), 143-156.
Z712.11015; M91h:11012

[8] Sums of products of Bernoulli numbers. J. Number Theory, 60 (1996), no. 1, 23-41.
Z863.11011; M97h:11014

DILCHER K., SKULA L.,
[1] A new criterion for the first case of Fermat's last theorem. Math. Comp. 64 (1995), no. 209, 363-392.
Z817.11022; M95c:11034

DILCHER K., SKULA L., SLAVUTSKII I. SH.,
[1] Bernoulli Numbers. Bibliography (1713-1990). Queen's Papers in Pure and Applied Mathematics, 87, Queen's University, Kingston, Ont., 1991.
Z741.11001; M92f:11001; R1992,4A54

DILCHER K.: see also BORWEIN J.M., BORWEIN P.B., DILCHER K.

DILCHER K.: see also AGOH T., DILCHER K., SKULA L.

DILCHER K.: see also CRANDALL R.E., DILCHER K., POMERANCE C.

DILLON J.F., ROSELLE D.P.,
[1] Eulerian numbers of higher order, Duke Math. J., 35 (1968), no. 2, 247-256.
Z185,30; M37#1261; R1969,1V229

DI MARZIO F.,
[1] The very accurate summation of inverse powers and the generation of Bernoulli and Euler numbers, Comput. Phys. Comm., 44 (1987), no. 1-2, 57-62.
Z673.10008; M88f:65014; R1988,2B36

DINTZL E.,
[1] Über Zahlen im Körper $k({\sqrt{-2)$, welche den Bernoullischen Zahlen analog sind, Sitz. Akad. Wiss., Wien, Math. und natur. Kl., 2e Abteil., 118 (1909), 173-201.
J40.265

[2] Über einige Eigenschaften der Bernoullischen und analoger Zahlen, Jb. k. k. Erzherzog-Rainer-Realgymnasium Wien, (1910), 1-11.
J(41.503)

[3] Über die Entwicklungscoeffizienten der elliptischen Funktionen, insbesondere im Falle singulärer Moduln, Monatsh. Math. und Physik, 25 (1914), 125-151.
J45.685

DITTRICH G.,
[1] Die Theorie des Fermat-Quotienten, Dissertation, Jena, 1924.

DOKOVIC D.,
[1] Formule pour le calcul des puissances semblables des nombres naturels, (Serbo-Croatian, French summary), Bull. Soc. Math. Phys. Macédoine 8 (1957), 38-40.
M23#A97

DOKSHITZER T.,
[1] On Wilf's conjecture and generalizations. In: Number Teory (K. Dilcher, Ed.), Fourth Conference of the Canadian Number Theory Association (Halifax, July 2-8, 1994), CMS Conference Proceedings 15, 133-153. Amer. Math. Soc., Providence, 1995.
Z837.11023; 96h:11031

DOLZE P.,
[1] Über Bernoullische Zahlen und Funktionen, welche zu einer Fundamentaldiskriminante gehören, und deren Anwendung auf die Summation unendlicher Reihen. Inaugurationsdissertation, Rostock, 44p. Dresden, 1907.
J37.500; 38.466

DONAGHEY R.,
[1] Binomial self-inverse sequences and tangent coefficients, J. Combin. Theory A, 21 (1976), no. 2, 155-163.
Z345.05002; M54#2475; R1977,3V372

DÖRFLER P.,
[1] A Markov type inequality for higher derivatives of polynomials, Monatsh. Math., 109 (1990), no. 2, 113-122.
Z713.41006; M91h:26017

DOWLING J.P.,
[1] The mathematics of the Casimir effect, Math. Magazine, 62 (1989), no. 5, 324-333.
M91a:81229

DRYANOV D., KOUNCHEV O.,
[1] Polyharmonically exact formula of Euler-Maclaurin, multivariate Bernoulli functions, and Poisson type formula, C. R. Acad. Sci. Paris Sér. I Math., 327 (1998), no. 5, 515-520.
Z908.65003; M99j:65003

DUCCI E.,
[1] Somma della potenze simili dei termini di una progressione per differenza, Giorn. Matem., Napoli, 23 (1894), 348-352.
J25.411

DUKE W., IMAMOGLU Ö.,
[1] Siegel modular forms of small weight, Math. Ann. 310 (1998), no. 1, 73-82.
Z892.11017; M98m:11037

DUMAS P., FLAJOLET P.,
[1] Asymptotique des récurrences mahlériennes: le cas cyclotomique, J. Théor. Nombres Bordeaux 8 (1996), no. 1, 1-30.
Z869.11080; M97f:39029

DUMONT D.,
[1] Sur une conjecture de Gandhi concernant les nombres de Genocchi, Discrete Math., 1 (1972), no. 4, 321-327.
Z263.10005; M45#5073; R1974,7B461

[2] Propriétés géométriques des nombres de Genocchi, Thèse, Strasbourg, 1973.

[3] Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318.
Z297.05004; M49#2412; R1985,3V437

[4] Conjectures sur des symétries ternaires liées aux nombres de Genocchi, Discrete Math., 139 (1995), no. 1-3, 469-472.
Z823.05003; M96e:05007

[5] Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers. Adv. in Appl. Math. 16 (1995), no. 3, 275-296.
Z834.05004; M96i:11021

DUMONT D., FOATA D.,
[1] Une propriété de symétrie des nombres de Genocchi, Bull. Soc. Math. France, 104 (1976), no. 4, 433-451.
Z362.05018; M55#7794

DUMONT D., RANDRIANARIVONY A.,
[1] Dérangements et nombres de Genocchi, Discrete Math., 132 (1994), no. 1-3, 37-49.
Z807.05001; M95h:05015

[2] Sur une extension des nombres de Genocchi, European J. Combin., 16 (1995), no. 2, 147-151.
Z823.05004; M96k:11015

DUMONT D., VIENNOT G.,
[1] A combinatorial interpretation of the Seidel generation of Genocchi numbers. Ann. Discrete Math., 6 (1980), 77-87.
Z449.10011; M82j:10024; R1981,8V588

DUMONT D., ZENG J.,
[1] Further results on the Euler and Genocchi numbers. Aequationes Math., 47 (1994), no. 1, 31-42.
Z805.11024; M95b:11021

[2] Polynômes d'Euler et fractions continues de Stieltjes-Rogers, Ramanujan J. 2 (1998), no. 3, 387-410.
M99i:05008

DUMONT D.: see also BARSKY D., DUMONT D.

DUPARC H.J.A., PEREMANS W.,
[1] On certain representations of positive integers, Nieuw. Arch. Wisk., 1 (1953), no. 2, 92-98.
Z50,269; M15-288e; R1954,2853

DUPUIS N.F.,
[1] Cruces mathematicae [Sect. 4: Expression of the general Bernoullian number as a combinational determinant]. Royal Society of Canada, Proc. and Trans. 7 (1889), Sect. 3, 15-22.

DUTKA J.,
[1] On the summation of some divergent series of Euler and the zeta functions. Arch. Hist. Exact Sci. 50 (1996), no. 2, 187-200.
Z858.01018; M98a:11112; R1997,5A6


EBBINGHAUS H.-D., HERMES H., HIRZEBRUCH F., KOECHER M., MAINZER K., NEUKIRCH J., PRESTEL A., REMMERT R.,
[1] Numbers, Springer-Verlag, Berlin etc., 1990, xviii+391pp.
Z705.00001,741.00003; M91h:00005

EDWARDS A.W.F.,
[1] Sums of powers of integers: a little of the history, Math. Gaz., 66 (1982), no. 435, 22-28.
Z493.10004; M83e:10013

EDWARDS H.M.,
[1] Riemann's zeta function, Academic Press, New York-London, 1974. xiii + 315 pp.
Z315.10035*; M57#5922; R1975,12A133K

[2] The background of Kummer's proof of Fermat's last theorem for regular primes, Arch. Hist. Exact. Sci., 14 (1975), no. 3, 219-236.
Z323.01022; M57#12066a; R1976,8A15

[3] Fermat's last theorem. A genetic introduction to algebraic number theory, Springer-Verlag, New York-Berlin, 1977. xv + 410 pp.
Z355.12001*; M83b:12001a; R1978,4A94K

[4] Postscript to:"The background of Kummer's proof of Fermat's last theorem for regular primes", Arch. History Exact Sci., 17 (1977), no. 4, 381-394.
Z364.01004; M57#12066b; R1978,6A15

[5] Fermat's last theorem, Sci. Amer., 239 (1978), no. 4, 104-122.

[6] Fermat's last theorem. (Bulgarian). Fiz.-Mat. Spis. B"lgar. Akad. Nauk., 22 (55)(1979), no. 4, 290-300 (1980).
Z462.10001; M82d:10002

EGORYCHEV G.P.,
[1] Integral representation and computation of combinatorical sums. (Russian) Izdat. "Nauka" Sibirsk. Otdel, Novosibirsk, 1977, 283 pp.
Z453.05001; M58#10474; R1978,3V444K

EIE MINKING [YÜ WÊN CH'ING],
[1] On the values at nonpositive integers of the Dedekind zeta function of a real quadratic field, Chinese J. Math., 15 (1987), no. 4, 215-226.
Z661.10031; M90e:11177

[2] On the values at negative half-integers of the Dedekind zeta function of a real quadratic field, Proc. Amer. Math. Soc., 105 (1989), no. 2, 273-280.
Z667.10013; M90a:11137; R1990,1A151

[3] On a Dirichlet series associated with a polynomial, Proc. Amer. Math. Soc., 110 (1990), no. 3, 583-590.
Z708.11040; M91m:11071; R1991,105139

[4] On the values at negative integers of zeta-functions associated with polynomials, Soochow J. Math., 16 (1990), no. 1, 53-61.
Z701.11030; M91k:11076

[5] The Maass space for Cayley numbers, Math. Z., 207 (1991), no. 4, 645-655.
Z737.11012; M92k:11053

[6] The special values at negative integers of Dirichlet series associated with polynomials of several variables, Proc. Amer. Math. Soc., 119 (1993), no.1, 51-61.
Z789.11052; M93k:11082

[7] A note on Bernoulli numbers and Shintani generalized Bernoulli polynomials. Trans. Amer. Math. Soc. 348 (1996), no. 3, 1117-1136.
Z864.11043; M96h:11011; M1996,8V251

EIE M., CHEN KWANG-WU
[1] A theorem on zeta functions associated with polynomials, Trans. Amer. Math. Soc. 351 (1999), no. 8, 3217-3228.
Z928.11038; M99m:11099

EIE M., KRIEG A.,
[1] The Maass space on the half-plane of Cayley numbers of degree two, Math. Z., 210 (1992), no.1, 113-128.
Z(729.11022); 757.11015; M93e:11063

EIE M., LAI K.F.,
[1] On Bernoulli identities and applications, Rev. Mat. Iberoamericana, 14 (1998), no. 1, 167-213.
M99h:11017

EIE M., ONG Y.L.,
[1] A generalization of Kummer's congruences, Abh. Math. Sem. Univ. Hamburg 67 (1997), 149-157.
Z896.11035; M98h:11024

EIE M.: see also FANG C.-H., EIE M.

EIGEL E.G., Jr.,
[1] Sums of powers of integers, Pi Mu Epsilon J., 4 (1964), 7-10.

EISENLOHE O.,
[1] Entwicklung der Functionsweise der Bernoullischen Zahlen, J. Reine Angew. Math., 28 (1844), 193-212.

ELIZALDE E.,
[1] An asymptotic expansion for the first derivative of the generalized Riemann zeta function, Math. Comp., 47 (1986), no. 175, 347-350.
Z603.10040; M87h:11081; R1987,2A95

[2] A simple recurrence for the higher derivatives of the Hurwitz zeta function. J. Math. Phys., 34 (1993), no. 7, 3222-3226.
Z779.11037; M94h:11078

ELY G.S.,
[1] Bibliography of Bernoulli's numbers, Amer. J. Math., 5 (1882), 228-235.
J15.21

[2] Some notes on the numbers of Bernoulli and Euler, Amer. J. Math., 5 (1883), 337-341.
J15.200

[3] On the numbers $a_{n,m}$, which occur in connection with the proof of Staudt's theorem concerning Bernoulli numbers, Johns Hopkins Univ. Circulars, 2 (1883), 47-48.
J15.204

ENDÔ A.,
[1] The relative class number of certain imaginary abelian fields, Abh. Math. Sem. Univ. Hamburg, 58 (1988), 237-243.
Z699.12015; M90m:11169; R1990,5A283

[2] The relative class number of certain imaginary abelian number fields and determinants, J. Number Theory, 34 (1990), no. 1, 13-20.
Z695.12004; M91b:11121

[3] On an index formula for the relative class number of a cyclotomic number field, J. Number Theory, 36 (1990), no. 3, 332-338.
Z715.11062; M91m:11092

[4] On the Stickelberger ideal of (2,...,2)-extensions of a cyclotomic number field, Manuscr. Math., 69 (1990), no. 2, 107-132.
Z715.11061; M91i:11144

[5] The relative class number of certain imaginary abelian number fields of odd conductors. Proc. Japan Acad. Ser. A Math. Sci. 72 (1996), no. 3, 64-68.
Z862.11062; M97e:11137; R1996,10A251

ENTRINGER R.C.,
[1] A combinatorial interpretation of the Euler and Bernoulli numbers, Nieuw Arch. Wisk. (3), 14 (1966), 241-246.
Z145,14; M34#5692; R1967,10V246

ERDÉLYI A., MAGNUS W., OBERHETTINGER F., TRICOMI F.,
[1] Higher transcendental functions. Vol. III., McGraw-Hill, New York, 1955. xvii + 292 pp.
Z64,63; M16-586c; R1957,3259K

ERDÖS P., WAGSTAFF S.,
[1] The fractional parts of the Bernoulli numbers, Illinois J. Math., 24 (1980), no. 1, 104-112.
Z(405.10011),449.10010; M81c:10064; R1980,11A108

ERNVALL R.,
[1] On the distribution $\pmod 8$ of the E-irregular primes, Ann. Acad. Sci. Fenniae, Ser. A1, Math., 1 (1975), no. 1, 195-198.
Z313.10010; M52#5594; R1976,10A98

[2] E-irregular primes and related tables, Math. Comp., 32 (1978), 656-657.

[3] Generalized Bernoulli numbers, generalized irregular primes, and class number, Ann. Univ. Turku., Ser. A1, (1979), no. 178, 1-72.
Z403.12010; M80m:12002; R1980,2A352

[4] Irregular primes (A lecture given in Finnish at the meeting of the Finnish Mathematical Society), Helsinki University of Technology Report Mat-C3, (1983), 7-14.

[5] Generalized irregular primes, Mathematika, 30 (1983), no. 1, 67-73.
Z(506,12007),514.12006; M85g:11022; R1984,5A126

[6] An upper bound for the index of $\chi$-irregularity, Mathematika, 32 (1985), no. 1, 39-44.
Z(555.12003),567.12007; M87e:11024

[7] A generalization of Herbrand's theorem, Ann. Univ. Turku. Ser. AI, 1989, no. 193, 15 pp.
Z658.12003; M90e:11159; R1989,10A319

[8] A note on the cyclotomic units, Comm. Math. Univ. St. Paul., 40 (1991), no. 1, 1-6.
Z742.11052; M92c:11118; R1992,5A266

[9] A congruence on Euler numbers (solution to a problem), Amer. Math. Monthly, 89 (1982), no. 6, 431.

ERNVALL R., METSÄNKYLÄ T.,
[1] Cyclotomic invariants and E-irregular primes, Math. Comp., 32 (1978), 617-629; corrig. Math. Comp., 33 (1979), 433.
Z(381.12002),398.12002; M80c:12004a,b; R1978,587

[2] A method for computing the Iwasawa $\lambda$-invariant, Math. Comp., 49 (1987), no. 179, 281-284.
Z(601.12010)616.12012; M88i:11080

[3] Cyclotomic invariants for primes between 125000 and 150000, Math. Comp., 56 (1991), no. 194, 851-858.
Z724.11052; M91h:11157

[4] Computations of the zeros of $p$-adic $L$-functions, Math. Comp., 58 (1992), no. 198, 815-830; S37-S53.
Z760.11021; M92j:11121; R1993,11A285; 1995,2A278

[5] Cyclotomic invariants for primes to one million, Math. Comp., 59 (1992), no. 199, 249-250.
Z760.11029; M93a:11108; R1993,10A296

[6] On the $p$-divisibility of Fermat quotients, Math. Comp. 66 (1997), no. 219, 1353-1365.
Z 970.26846; M97i:11003; R1998,5A91

ERNVALL R.: see also BUHLER J.P. et al

ESTANAVE E.,
[1] Sur les coefficients des développements en série de tang $x$, sec$x$ et d'autres fonctions, Bull. Soc. Math. France, 30 (1902), 220-226.
J33.290

ESTERMANN T.,
[1] Elementary evaluation of $\zeta(2k)$, J. London Math. Soc., 22 (1947), no. 1, 10-13.
Z29.394; M9-234d

ETTINGSHAUSEN A.,
[1] Vorlesungen über die höhere Mathematik Bd. 1, Vienne, (1827).

EULER L.,
[1] Methodus generalis summandi progressiones, Comment. Acad. Sci. Petropol., 6 (1732/33), (1738), 68-97.

[2] De summis serierum reciprocarum, Comment. Acad. Sci. Petropol., 7 (1734/35), (1740), 123-134.

[3] Inventio summae cujusque seriei ex dato termino generali, Comment. Acad. Sci. Petropol., 8 (1736), (1741), 9-22.

[4] Consideratio progressiones cujusdam ad circuli quadraturam inveniendam idoneae, Comment. Acad. Sci. Petropol., 11 (1739), (1750), 116-127.

[5] De seriebus quibusdam considerationes, Comment. Acad. Sci. Petropol., 12 (1740), (1750), 53-96.

[6] Introductio in analysin infinitorum, Lausannae, 1748.

[7] Institutiones Calculi Differentialis, Petersburg, 1755.

[8] De curva hypergeometrica hac aequatione expressa $y = 1.2 \cdots x$, Novi Comment. Acad. Sci. Petropol., 13 (1768), (1769), 3-66.

[9] De summis serierum numeros Bernoullianos involventium, Novi Comment. Acad. Sci. Petropol., 14 (1769), (1770), 129-167.

[10] De numero memorabili in summatione progressionis harmonicae naturalis occurrente, Acta. Acad. Petropol., p.2 (1781), (1785), 458-75.

[11] De seriebus potestatum reciprocis methodo nova et facillima summandis. Opuscula analytica, 2 (1785), 257-274 = Opera Omnia, I.15, Teubner, Leipzig-Berlin, 1927, 701-722.

EVANS R.J.: see BERNDT B.C., EVANS R.J.

EVANS R.J.: see BERNDT B.C., EVANS R.J., WILSON B.M.

EWELL J.A.,
[1] On values of the Riemann zeta function at integral arguments, Canad. Math. Bull., 34 (1991), no. 1, 60-66.
Z731.11048; M92c:11087

EYTELWEIN J.A.,
[1] Ueber die Vergleichung der Differenz-Coefficienten mit den Bernoulli'schen Zahlen, Abhandl. Kgl. Preuss. Akad. Wiss., Math. Kl., (1816/17) (1819), 28-41.

[2] Grundlehren der höheren Analysis, Berlin, Bd. 2, 1824.

EZHOV I.I.,
[1] Bernoulli numbers and some of their applications. (Russian), Krasnojarsk. Gos. Univ., Krasnoyarsk, 1976, 109-115
M58#27735; R1977,11V539

[2] Bernoulli numbers and Chebyshev problems for primes. (Russian), Dokl. Akad. Nauk. Ukrain. SSSR Ser. A, (1981), no.6, 12-15.
Z459.10003; M83f:10047; R1981,11A81


FANG C.-H., EIE M.,
[1] On the values of a zeta function at non-positive integers, Pacific J. Math., 145 (1990), no. 2, 201-210.
Z733.11031; M92d:11034; R1991,6A78

FEINLER F.J.,
[1] A new method for calculating the Bernoulli numbers, Mess. Math., 55 (1925), 40-44.
J(51.77)

[2] Recurrence formulas for the Bernoulli numbers derived from zero differences (Abstract), Bull. Amer. Math. Soc., 32 (1926), 126.
J(52.361)

FENDER W.,
[1] Zur Theorie von verallgemeinerten Bernoullischen und Eulerschen Zahlen, Dissertation, Universität Jena, (1911), 58p.
J42.458

FENG KE QIN,
[1] The Ankeny-Artin-Chowla formula for cubic number field (Chinese, English summary), J. China Univ. Sci. Tech., 12 (1982), no. 1, 20-27.
M85a:11018

[2] A note on irregular prime polynomials in cyclotomic functional field theory, J. Number Theory, 22 (1986), no.2, 240-245.
Z578.12012; M87g:11156; R1986,8A325

FENG KE QIN, GAO W.Y.,
[1] Bernoulli-Goss polynomial and class number of cyclotomic function fields, Sci. China Ser. A, 33 (1990), no. 6, 654-662.
Z708.11064; M91m:11099

FERGOLA E.,
[1] Sopra la sviluppo della funzione $1\over{ce^x-1$ e sopra una nuovo expressione dei numeri di Bernoulli, Mem. Accad. Sci., Napola, 2, (1855/57), 315-324.

FERGUSON H.R.P.,
[1] Bernoulli numbers and non-standard differentiable structures on $(4k-1$)-spheres, Fibonacci Quart., 11 (1973), no. 1, 1-14.
Z225.10012; M46#7134; R1973,9A537

FERRERO B.,
[1] Iwasawa invariants of abelian number fields, Thesis, Princeton Univ., 1975.

[2] An explicit bound for Iwasawa's $\lambda$-invariant, Acta Arith., 33 (1977), no. 4, 405-408.
Z(323.12004)355.12002; M56#15605; R1978,7A460

FERRERO B., GREENBERG R.,
[1] On the behaviour of p-adic L-functions at $s=0$, Invent. Math., 50 (1978), no. 1, 91-102.
Z441.12003; M80f:12016; R1979,7A402

FERRERO B., WASHINGTON L.C.,
[1] The Iwasawa invariant $\mu_p$ vanishes for abelian number fields, Ann. of Math. (2), 109 (1979), no. 2, 377-395.
Z443.12001; M81a:12005; R1979,12A379

FIELDS J.C.,
[1] Related expressions for Bernoulli's and Euler's numbers, Amer. J. Math., 13 (1891), 191-192.
J22.266

FIKHTENGOLTS G.M.,
[1] Kurs differentsial'nogo i integral'nogo ischisleniya [A course in differential and integral calculus], Vol. 2, Ch. 12. Moscow, 1948.
Z33.107

FILLEBROWN S.,
[1] Faster computation of Bernoulli numbers, J. Algorithms, 13 (1992), no. 3, 431-445.
Z755.11006; M94d:68044

FLAJOLET P.,
[1] On congruences and continued fractions for some classical combinatorial quantities, Discrete Math., 41 (1982), no. 2, 145-153.
M84f:05005; R1983,2A58

FLAJOLET P., PRODINGER H.,
[1] On Stirling numbers for complex arguments and Hankel contours. SIAM J. Discrete Math. 12 (1999), no. 2, 155-159.
R921.05001

FLAJOLET P.: see DUMAS P., FLAJOLET P.

FLETCHER A., MILLER J.C.P., ROSENHEAD L., COMRIE L.J.,
[1] An Index of Mathematical Tables, Vol. I, II, 2nd ed. Addison Wesley Publ. Co., Inc., Reading, Mass., 1962. xi + pp. 1-608; iv + pp. 609-994.
M26#365a,b; R1963,7V44K

FLOCKE S.: see BUTZER P.L., FLOCKE S., HAUSS M.

FOATA D.,
[1] Propriétés arithmétiques des polynômes d'Euler. Séminaire Delange-Pisot-Poitou, No. 20 (1967/68).
Z272.05006; R1969,9A79

[2] Groupes de réarrangements et nombres d'Euler, C.R. Acad. Sci. Paris Sér. A, 275 (1972), 1147-1150.
Z269.20006; M47#8320; R1973,11V421

[3] Réarrangements d'applications associées aux nombres de Genocchi, C. R. des Journées Mathématiques de la Société Math. de France, pp. 113-121. Cahiers Math. Montpellier, no. 3, U. E. R. de Math., Univ. Sci. Tech. Languedoc, Montpellier, 1974.
M51#12542

FOATA D., SCHÜTZENBERGER M.-P.,
[1] Théorie Géométrique des Polynômes Eulériens. Lecture Notes in Mathematics, No. 138. Springer-Verlag, Berlin-Heidelberg- New York, 1970.
Z214,262; M42#7523; R1971,1V267

[2] Nombres d'Euler et permutations alternantes. In: A Survey of Combinatorial Theory, 173-187. North-Holland, Amsterdam, 1973.
Z271.05005; M50#6870; R1974,4V272

FOATA D., STREHL V.,
[1] Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers, Math. Z., 137 (1974), 257-264.
Z274.05007; M50#450; R1975,3V447

[2] Euler numbers and variations of permutations, Colloquio Internazionale sulle Teorie Combinatorie (Roma, 1973), Tomo I, 119-131. Atti dei Convegni Lincei, No. 17, Accad. Naz. Lincei, Roma, 1976.
Z361.05010; M55#7795

FOATA D.: see also ANDREWS G., FOATA D.

FOATA D.: see also DUMONT D., FOATA D.

FORDER H.G.,
[1] Euler numbers, Math. Gazette, 14 (1928/29), 233.
J54.182

FORRESTER P.J.,
[1] Extensions of several summation formulae of Ramanujan using the calculus of residues, Rocky Mountain J. Math., 13 (1983), no. 4, 557-572.
Z537.10007; M85i:40004

FORT T.,
[1] Generalizations of the Bernoulli polynomials and numbers and corresponding summation formulas, Bull. Amer. Math. Soc., 48 (1942), no. 8, 567-574.
Z61,199; M4-79f

[2] An addition to "Generalizations of the Bernoulli polynomials and numbers and corresponding summation formulas", Bull. Amer. Math. Soc., 48 (1942), 949.
M4-79g

FOUCHÉ W.,
[1] A reciprocity law for polynomials with Bernoulli coefficients, Trans. Amer. Math. Soc., 288 (1985), no. 1, 59-67.
Z558.10013; M86d:11085; R1986,1A387

[2] On the p-adic zeros of polynomials with Bernoulli coefficients, Arch. Math., 45 (1985), no. 6, 534-537.
Z(563.10013)573.10012; M87b:11019; R1986,6A193

[3] On the Kummer-Mirimanoff congruences, Quart. J. Math. (Oxford)(2), 37 (1986), no. 147, 257-261.
Z604.10007; M88a:11022; R1987,12A73

[4] The distribution of Bernoulli numbers modulo primes, Arch. Math., 50 (1988), no. 2, 139-144.
Z644.10011; M89d:11011; R1988,8A101

FOULKES H.O.,
[1] Tangent and secant numbers and representations of symmetric groups, Discrete Math., 15 (1976), no. 4, 311-324.
M53#10596; R1976/77,2V444

FOX, G.J.,
[1] A $p$-adic $L$-function of two variables, Ph.D. thesis, University of Georgia, Athens, Georgia, 1997, 156pp.

[2] Euler polynomials at rational numbers, C. R. Math. Acad. Sci. Soc. R. Can. 21 (1999), no. 3, 87-90.

FRAENKEL A.S.,
[1] A characterization of exactly covering congruences, Discrete Math., 4 (1973), no. 4, 359-366.
Z257.10003; M47#4906; R1973,11A101

[2] Further characterizations and properties of exactly covering congruences, Discrete Math., 12 (1975), no. 1, 93-100.
Z306.10002; M51#10276; R1975,11V357

FRAME J.S.,
[1] Euler and tangent numbers and the exponential shift, Amer. Math. Monthly, 67 (1960), 1016-1019.
R1961,10A151

[2] Bernoulli numbers modulo 27000, Amer. Math. Monthly, 68 (1961), 87-95.
Z134,274; M23#A1586; R1962,1A146

[3] The Hankel power sum matrix inverse and the Bernoulli continued fraction, Math. Comp., 33 (1979), no. 146, 815-826.
Z419.65029; M80f:65044; R1980,1A406

[4] Primes, ratios, and Bernoulli numbers (problem), Amer. Math. Monthly, 90 (1983), no. 9, 645-646.

[5] More like $\zeta(2[n/2])$ than $\zeta(2n)$ (problem), Amer. Math. Monthly, 93 (1986), 744-745.

FRANÇON J., VIENNOT G.,
[1] Permutations selon leurs pics, creux, doubles montées et doubles descentes, nombres d'Euler et nombres de Genocchi, Discrete Math., 28 (1979), no. 1, 21-35.
Z409.05003; M81a:05002; R1980,5V425

FRANSÉN A.,
[1] Properties of Stirling polynomials and a disproof of Robertson's conjecture, J. Math. Anal. Appl., 154 (1991), no. 2, 446-451.
Z729.30002; M92d:11016

FRAPPIER C.,
[1] Representation formulas for entire functions of exponential type and generalized Bernoulli polynomials, J. Austral. Math. Soc. Ser. A, 64 (1998), no. 3, 307-316.
Z909.30018; M99i:30045

FRESNEL J.,
[1] Congruences entre les nombres de Bernoulli, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 6 (1964/65), (1967), no. 14, 1-12.
Z206,336; M35#6505; R1968,5A206

[2] Nombres de Bernoulli et fonctions L p-adiques, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 7 (1965/66), (1967), no. 14, 1-15.
Z247.12013; M35#6507; R1968,5A189

[3] Les fonctions p-adiques L de Dirichlet, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 7 (1965/66), (1967), no. 17, 1-8.
Z222.12017; M35#6505; R1968,5A190

[4] Nombres de Bernoulli généralisés et fonctions L p-adiques, C.R. Acad. Sci., Paris, 263 (1966), 337-340.
Z147,22; M34#1304; R1968,4V272

[5] Applications arithmétiques de la formule p-adique des résidus, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 8 (1966/67), (1968), no. 18, 1-8.
Z162,70; R1969,3A277

[6] Nombres de Bernoulli et fonctions L p-adiques, Ann. Inst. Fourier, 17 (1967), (1968), 281-333.
Z157,103; M37#169; R1968,9A121

[7] Fonctions zêta p-adiques des corps de nombres abéliens réels, Bull. Soc. Math. France, Mém. No. 25, 1971, pp. 83-89.
Z242.12009; M52#3121; R1972,3A321

FRESNEL J.: see also AMICE Y., FRESNEL J.

FRICKE A.,
[1] Die Potenzsummenformel und ihre Struktur, Prax. Math., 29 (1987), no. 8, 462-470.
M89k:40008; R1988,7A103

FRIEDMAN E.C.,
[1] Ideal class group in basic $ Z_{p_1 \times \cdots \times Z_{p_t}$-extension of abelian number fields, Invent. Math., 65 (1982), no. 3, 425-440.
Z495.12007; M83i:12007; R1982,6A322

FRIEDMAN E., SANDS J. W.,
[1] On the $l$-adic Iwasawa $\lambda$-invariant in a $p$-extension. With an appendix by Lawrence C. Washington. Math. Comp. 64 (1995), no. 212, 1659-1674.
Z854.11055; M96a:11116; R1996,4A268

FRIEDMANN A.A., TAMARKINE J.,
[1] Sur les congruences du second degré et les nombres de Bernoulli, Math. Ann., 62 (1906), no. 3, 409-412.
J37.228

[2] Quelques formules concernant la théorie de la fonction $[x]$ et des nombres de Bernoulli, J. Reine Angew. Math., 135 (1908), 146-156.
J39.262

FROBENIUS G.,
[1] Über den Fermatschen Satz, Sitzungsber. Preuss. Akad. Wiss. Berlin (1909), 1222-1224. = J. Reine Angew. Math., 137 (1910), 314-316. = Gesammelte Abhandlungen, Springer, Berlin, Bd. 3, 1968, 428-430.
J41.236

[2] Über den Fermatschen Satz, II, Sitzungsber. Preuss. Akad. Wiss. Berlin, (1910), 200-208. = Gesammelte Abhandlungen, Springer, Berlin, Bd. 3, 1968, 431-439.
J41.236

[3] Über die Bernoullischen Zahlen und die Eulerschen Polynome, Sitzungsber. Preuss. Akad. Wiss., (1910), no. 2, 809-847; Ges. Abhandlungen, Berlin: Springer, Bd. 3, 1968, 440-478.

[4] Über den Fermatschen Satz, III, Sitzungsber. Preuss. Akad. Wiss., (1914), N 22, 653-681; Ges. Abhandlungen, Berlin e.a.: Springer, Bd. 3, 1968, 648-676.
J45.290

FUETER R.,
[1] Kummers Kriterium zum letzten Theorem von Fermat, Math. Ann., 85 (1922), 11-20.
J48.130

FUJII A.,
[1] Some problems of Diophantine approximation in the theory of the Riemann zeta function. Proc. Japan Acad. Ser. A Math. Sci., 68 (1992), no. 6, 131-136.
Z795.11034; M93g:11093

[2] Some problems of Diophantine approximation in the theory of the Riemann zeta function. II. Proc. Japan Acad. Ser. A Math. Sci., 69 (1993), no. 4, 85-90.
Z804.11049; M94b:11084

[3] Some problems of Diophantine approximation in the theory of the Riemann zeta function. III. Comment. Math. Univ. St. Paul., 42 (1993), no. 2, 161-187.
Z805.11058; M94i:11065

[4] On the zeros of the Epstein zeta functions, J. Math. Kyoto Univ. 36 (1996), no. 4, 697--770.
Z970.52672; M98e:11049

FUJISAKI G.,
[1] A generalization of Carlitz's determinant, Sci. Pap. College Arts Sci. Univ. Tokoyo, 40 (1991), no. 2, 63-68.
Z722.11014; M91m:11012; R191,10A220

FUJIWARA M.,
[1] Sur les nouveaux nombres de M. Pascal, Rom. Acc. L. Rend. (5), 17 (1908), 401-405.
J39.264

FUKUHARA S.,
[1] The space of period polynomials, Acta Arith. 82 (1997), no. 1, 77-93.
Z881.11046; M99i:11027

[2] Generalized Dedekind symbols associated with the Eisenstein series. Proc. Amer. Math. Soc. 127 (1999), no. 9, 2561-2568.
Z924.11030; M2000a:11061

FUNG. G., GRANVILLE A., WILLIAMS H.C.,
[1] Computation of the first factor of the class number of cyclotomic fields, J. Number Theory, 42 (1992), no. 3, 297-312.
Z762.11039; M93k:11097


GADIA S.K.: see GANDHI J.M., GADIA S.K.

GAJDA W.: see BANASZAK G., GAJDA W.

GAMBIOLLI D.,
[1] Memoria bibliografica sull'ultimo theorema di Fermat, Periodico di Mat. (2), 3 (1901), 145-192.
J32.45

[2] Appendice alla mia memoria bibliografica sull'ultimo theorema di Piotro Fermat, Periodico di Mat., 4 (1901), 48-50.
J32.196

GANDHI J.M.,
[1] The coefficients of $cosh x/cos x$ and a note on Carlitz's coefficients of $sinh x/sin x$, Math. Mag., 31 (1958), no. 4, 185-191.
Z99,264; M20#5301; R1959,2326

[2] Some integrals for Genocchi numbers, Math. Mag., 33 (1959), no. 1, 21-23.
Z92,57; M21#5751; R1960,13047

[3] A new formula for Genocchi Numbers, Math. Student, 28 (1960), (1962), 83-85.
Z115,29; M26-45; R1962,11A109

[4] Generalized Fermat's last theorem and regular primes, Proc. Japan Acad., 46 (1970), 626-629.
Z225.10016; M44#2701; R1971,9A94

[5] The coefficients of $sinh x/cos x$, Can. Math. Bull., 13 (1970), no. 3, 305-310.
Z207,24; M42#7588; R1971,4A83

[6] A conjectured representation of Genocchi numbers, Amer. Math. Monthly, 77 (1970), no. 5, 505-506.
Z198,370; R1971,1A100

[7] On generalized Fermat's last theorem. II. J. Reine Angew. Math., 256 (1972), 163-167.
Z248.10028; M47#8426; R1973,3A177

[8] Euler's numbers and the Diophantine equation $x^l + y^l = z^lc$, Acta Arith., 24 (1973), 21-26.
Z227.10009; M47#1736; R1973,11A134

[9] Congruences for Genocchi numbers, Duke Math. J., 31 (1964), 519-527.
M29#2210; R1965,6A127

GANDHI J.M., GADIA S.K.,
[1] A simple proof of the infinity of irregular primes. Proc. 7th Manitoba Conf. on Numer. Math. and Comp., Congress. Numer., XX, Utilitas Math., Winnipeg, 1978, pp. 379-382.
Z482.10012; M80h:10010

GANDHI J.M., KASUBE H., SURYANARAYANA D.,
[1] Congruences for Bernoulli numbers modulo $p^3$, Boll. Union. Mat. Ital., (1978), A 15, no. 3, 517-525.
Z391.10015; M80j:10017; R1979,7A134

GANDHI J.M., SINGH A.,
[1] Fourth interval formulae for the coefficients of $cosh x/cos x$, Monatsh. Math., 70 (1966), no. 4, 327-329.
Z141,259; M33#5504; R1967,4B6

GANDHI J.M., TANEJA V.S.,
[1] The coefficients of $cosh x/cos x$, Fibonacci Quart., 10 (1972), no. 4, 349-353.
Z248.10012; M46#7140; R1973,4V385

GAO W.Y.: see FENG KE QIN, GAO W.Y.

GARABEDIAN H.L.,
[1] A new formula for the Bernoulli numbers, Bull. Amer. Math. Soc., 46 (1940), 531-533.
J66.319; Z63.I.309; M2-88e

GARDINER A.,
[1] Four problems in prime power divisibility, Amer. Math. Monthly, 95 (1988), 926-931.
Z663.10002; R1989,10A105

GAWRILOWISCH A.,
[1] Über die Bernoullischen und Eulerschen Zahlen, Veröffentl. Kgl. Serbischen Akad., Belgrad, 63 (1902), 113-142 (serb.).
J33.291

GEGENBAUER L.,
[1] Arithmetische Note, Sitzungsber. Math.-Natur. Kl. Akad. Wiss., Wien, 96 (1887), 491-496.

[2] Notiz über die zu einer Fundamentaldiscriminante gehörigen Bernoullischen Zahlen, Sitzungsber. Math.-Natur. Kl. Akad. Wiss., Wien, 102 (1893), 1059-1069.
J15.416

GEKELER E.-U.,
[1] Some new identities for Bernoulli-Carlitz numbers, J. Number Theory, 33 (1989), no. 2, 209-219.
Z697.12012; M90j:11128; R1990,5A284

[2] On regularity of small primes in function fields, J. Number Theory, 34 (1990), no. 1, 114-127.
Z695.12008; M91a:11060; R1990,5A284

GELFAND M.B.,
[1] A note on a certain relation among Bernoulli numbers. (Russian), Bashkir. Gos. Univ. Uchen. Zap., 31 (1968), Ser. Mat., no. 3, 215-216.
M43#7399; R1968,7V286

GELFOND A.O.,
[1] The calculus of finite differences. (Russian). Gosudarstv. Izdat. Tekhn.-Teor. Lit., Moscow-Leningrad, (1952), 479 pp.
Z96,282; M14-759d; R1961,1B322K

[2] Residues and its applications. (Russian). Izdat. "Nauka", Moscow, (1966), 112 pp.
Z152,59; M36#5310; R1968,5B158K

GENG JI,
[1] Bernoulli numbers and Euler numbers - a discussion on two properties of power series (Chinese), Math. Practice Theory 1991, no.3, 85-92.

GENOCCHI A.,
[1] Intorno all'espressione generale de'numeri Bernoulliani, Annali sci. mat. e fis., Roma, 3 (1852), 395-405.

[2] Sulla formula sommatoria di Eulero, e sulla teorica de' residui quadratici, Annali sci. mat. e fis., Roma, 3 (1852), 406-436.

[3] Sur la formule sommatoire de Maclaurin et les fonctions interpolaires, C.R. Acad. Sci., Paris, 86 (1878), 466-469.
J10.178

[4] Sur les nombres de Bernoulli (extrait d'une lettre à M. Kronecker), J. Reine Angew. Math., 99 (1886), 315-316.
J18.228

GERONIMUS J.,
[1] On a class of Appell polynomials, Commun. Soc. Math. Kharkoff et Inst. Sci. Math. et Mécan., Univ. Kharkoff (4), 8 (1934), 13-23.
J60.I.292; Z10,261

GERTSCH A.,
[1] Nombres harmoniques généralisés, C. R. Acad. Sci. Paris Sér. I Math., 324 (1997), no. 1, 7-10.
Z877.11010; M98a:11007; R1997,10A128

GESSEL I.,
[1] Congruences for Bell and tangent numbers, Fibonacci Quart., 19 (1981), no. 2, 137-143.
Z451.10008; M82f:10014; R1981,11V490

[2] Some congruences for generalized Euler numbers, Can. J. Math., 35 (1983), no. 4, 687-709.
Z493.10014; M85f:11013; R1984,10A69

[3] A Bernoulli recurrence (Solution to Problem E3237, proposed by J.G.F. Belinfante), Amer. Math. Monthly, 96 (1989), no. 4, 364-365.

[4] Generating functions and generalized Dedekind sums, Electron. J. Combin. 4 (1997), no. 2, Research Paper 11, approx. 17 pp. (electronic).
M98f:11032

GESSEL I., MATTICS L.E.,
[1] Numerators and denominators of Bernoulli numbers (solution to problem), Amer. Math. Monthly, 90 (1983), no. 8, 568-569.

GESSEL I.: see also ANDREWS G., GESSEL I.

GILBERT Ph.,
[1] Observations sur deux notes de M. Genocchi, relatives au développement de la fonction $\log{\Gamma (x)$, Bull. Acad. Sci. Bruxelles, 36 (1873), 541-545.
J5.167

GILLARD R.,
[1] $ Z_l$-extensions, fonctions L $l$-adiques et unités cyclotomiques. Séminaire de Théorie des Nombres (1976-77), Exp. No. 24, 19 pp., CNRS, Talence, 1977.
Z392.12006; M80k:12016

GILLARD R.: see also CHARKANI EL HASSANI M., GILLARD R.

GILLESPIE F.S.,
[1] A generalization of Kummer's congruences and related results, Fibonacci Quart., 30 (1992), no. 4, 349-367.
Z762.11004; M93i:11026

GIRGENSOHN R.: see BAILEY D.H., BORWEIN J.M., GIRGENSOHN R.

GIRGENSOHN R.: see also BORWEIN D., BORWEIN J.M., BORWEIN P.B., GIRGENSOHN R.

GIRSTMAIR K.,
[1] Ein v. Staudt-Clausenscher Satz für periodische Bernoulli-Zahlen, Monatsh. Math., 104 (1987), no. 2, 109-118.
Z626.12001; M89a:11026; R1988,4A79

[2] Character coordinates and annihilators of cyclotomic numbers, Manuscr. Math., 59 (1987), no. 3, 375-389.
Z624.12006; M89a:11071; R1988,3A418

[3] An index formula for the relative class number of an abelian number field, J. Number Theory, 32 (1989), no. 1, 100-110.
Z675.12002; M91d:11132; R1990,2A333

[4] A theorem on the numerators of the Bernoulli numbers, Amer. Math. Monthly, 97 (1990), no. 2, 136-138.
Z738.11023; M91a:11015; R1990,11A83

[5] Dirichlet convolution of cotangent numbers and relative class number formulas, Monatsh. Math., 110 (1990), no. 3/4, 231-256.
Z717.11048; M92b:11076; R1991,7A291

[6] Eine Verbindung zwischen den arithmetischen Eigenschaften verallgemeinerter Bernoullizahlen, Expos. Math., 11 (1993), 47-63.
Z773.11013; M94f:11011

[7] On the factorization of the relative class number in terms of Frobenius divisions. Monatsh. Math., 116 (1993), no. 3-4, 231-236.
Z802.11044; M95b:11105

[8] The relative class numbers of imaginary cyclic fields of degrees 4, 6, 8 and 10. Math. Comp., 61 (1993), no. 204, 881-887.
Z787.11046; M94a:11170

[9] Class number factors and distribution of residues, Abh. Math. Sem. Univ. Hamburg, 67 (1997), 65-104.
Z889.11032

GLAISHER J.W.L.,
[1] On the constants that occur in certain summations by Bernoulli's numbers, Proc. Lond. Math. Soc., 4 (1872), 48-56.
J4.109

[2] On a deduction from Von Staudt's property of Bernoulli's numbers, Proc. Lond. Math Soc., 4 (1872), 212-214.
J4.109

[3] On the function which stands in the same relation to Bernoulli's numbers that the gamma function does to factorials, Report Brit. Assoc., 42 (1872), 17-19.
J4.72

[4] On semi-convergent series, Quart. J. Math., 12 (1872), 52-58.
J4.102

[5] Tables of the first 250 Bernoulli's numbers (to nine figures) and their logarithms (to ten figures), Trans. Camb. Phil. Soc., 12 (1873), 384-391.
J5.144

[6] Simple proof of a known property of Bernoulli's numbers, Messeng. Math. (2), 2 (1873), 190-191.
J5.144

[7] Arithmetical proof of Clausen's Identity, Messeng. Math. (2), 6 (1875), 83.
J7.132

[8] Expressions for Laplace's coefficients, Bernoullian and Eulerian numbers, etc., as determinants, Mess. Math., 6 (1877), 49-63; 7 (1878), 160-165; 8 (1879), 158-167.
J8.306

[9] On the numerical value of a certain series, Proc. London Math. Soc., 8 (1877), 200-204.
J9.181

[10] Theorem relating to sums of even powers of the natural numbers, Messeng. Math., 20 (1890), 120-128.
J22.269

[11] Note on series whose coefficients involve powers of the Bernoullian numbers, Messeng. Math., 19 (1890), 138-146.
J22.269

[12] Recurring relations involving sums of powers of divisors, Messeng. Math., 20 (1891), 129-135; 177--181; 21, 49-64.
J23.177

[13] Note on the sums of even and uneven numbers, Messeng. Math., 20 (1891), 172-176.
J23.269

[14] On the sums of inverse powers of the prime numbers, Quart. J. Math., 25 (1891), 347-362.
J23.275

[15] Calculation of the hyperbolic logarithm of $\pi$ to thirty decimal places, Quart. J. Math., 25 (1891), 362-368, 384.
J23.277

[16] On the series $\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+ \frac{1}{11}+\&c.$, Quart. J. Math., 25 (1891), 369-383.

[17] Relations between the divisors of the first $n$ numbers, Proc. London Math. Soc., 22 (1891), 359-410.
J23.177

[18] On the definite integrals connected with the Bernoullian function, Mess. Math., 26 (1897), 152-182; 27 (1898), 20-98.

[19] On the Bernoullian function, Quart. J. Pure Appl. Math., 29 (1898), 1-168.
J28.375

[20] Note on a theorem relating to sums of even powers of the natural numbers, Messeng. Math. (2), 28 (1899), 29-32.
J29.220

[21] Classes of recurring formulae involving Bernoullian numbers, Messeng. Math., 28 (1899), 36-79.
J29.220

[22] On the values of the series $x^n + (x-q)^n+(x-2q)^n+...+r^n$ and $x^n-(x-q)^n+(x-2q)^n -...\pmr^n$, Quart. J. Math., 31 (1899), 193-227.
J30.254

[23] On $1^n(x-1)^n+2^n(x-2)^n+...+(x-1)^n1^n$ and other similar series, Quart. J. Math., 31 (1899), 241-247.
J30.254

[24] On the residues of the sums of the inverse powers of numbers in arithmetical progression, Quarterly J. Math., 32 (1900), 271-288.
J31.186

[25] Fundamental theorem relating to the Bernoullian numbers, Messeng. Math., 29 (1900), 49-63; 129-142.
J30.182; 31.287

[26] On the residues of the sums of products of the first $p-1$ numbers and their powers, to modulus $p^2$ or $p^3$, Quart. J. Math., 31 (1900), 321-353.
J31.195

[27] A congruence theorem relating to the Bernoullian numbers, Quart. J. Math., 31 (1900), 253-263.
J30.180

[28] Note on the residues of the ratios of certain series of inverse powers of numbers in arithmetical progression, Mess. Math., 30 (1901), 154-162.

J30.200

[29] On the residue to modulus p, of $1+1/3^{2n}+1/5^{2n}+...+1/(p-2)^{2n}$, Mess. Math., 30 (1901), 26-31.

[30] A general congruence theorem relating to the Bernoullian function, Proc. London Math. Soc., 33 (1901), 27-56.
J32.199

[31] On the residues of Bernoullian functions for a prime modulus, including as special cases the residues of Bernoullian, Eulerian and J-Numbers, Proc. London Math. Soc., 33 (1901), 56-87.
J32.199

[32] On a class of relations connecting any n consecutive Bernoullian functions, Part III. Quart. J. Pure Appl. Math., 42 (1911), 86-157.
J41.495

[33] On $1^n(x-1)^m+...+(x-1)^n1^m$ and other similar series, Quart. Journ. Math., 43 (1912), 101-122.
J43.340

[34] A congruence theorem relating to Eulerian numbers and other coefficients, Proc. London Math. Soc., 32 (1901), 171-198.

[35] Expansion of $(e^x-a)^{-1}$ and derived formulae; also values of $(d/d\theta)^n\tan \theta$, Mess. Math. (2), 39 (1910), 154-173.
J41.497

[36] Bernoullian numbers and other coefficients expressed in terms of numbers of the form $\Delta^n 0^n$, Quart. J. Pure Appl. Math., 41 (1910), 265-301.
J41.495

[37] On the last two figures in certain coefficients analogous to the Eulerian numbers, Quart. J. Pure Appl. Math., 44 (1913), 105-112.
J44.320

[38] On Eulerian numbers (formulae, residues, endfigures) with the values of the first twenty-seven, Quart. J. Pure Appl. Math., 45 (1913), 1-51.
J44.320

[39] Numerical values of the series $1-\frac{1}{3^n}+\frac{1}{5^n}- \frac{1}{7^n}+\frac{1}{9^n}-$ \&c., Mess. Math. (2), 42 (1913), 35-58.

GOHIERRE DE LONGCHAMPS: see LONGCHAMPS G.

GOLD R.: see CHILDRESS N., GOLD R.

GOLDSTEIN L.J., RAZAR M.J.,
[1] Ramanujan type formulae for $\zeta (2k-1)$, J. Pure Appl. Algebra, 13 (1978), no. 1, 13-17.
Z391.10023; M80f:10048; R1979,3A100

[2] The theory of zeta functions of several complex variables, I, J. Number Theory, 19 (1984), no. 2, 148-175.
Z549.12007; M86b:11078; R1985,6A94

GOLOVINSKII I.A.
[1] The Euler-Boole summation formula. (Russian), Istor.-Mat. Issled., no. 26, (1982), 52-91.
Z518.01004; M84k:01029; R1985,7A10

GOMES TEIXEIRA F.: see TEIXEIRA F.G.

GÖPEL A.,
[1] Einige Bermerkungen zu der Abhandlung Nr. IV in diesem Hefte über Recursionsformeln für die Bernoullischen Zahlen, Archiv d. Math. u. Physik, 3 (1843), 64-67.

GOSPER R.W., ISMAIL M.E.H., ZHANG R.,
[1] On some strange summation formulas. Illinois J. Math., 37 (1993), no. 2, 240-277.
Z793.33016; M95g:33025

GOSS D.,
[1] Von Staudt for $F_q(T)$, Duke Math. J., 45 (1978), no. 4, 887-910.
Z404.12013; M80a:12019; R1979,9A338

[2] The $\Gamma$-ideal and special zeta-values, Duke Math. J., 47 (1980), no. 2, 345-364.
Z441.12002; M81k:12015; R1981,3A338

[3] A simple approach to the analytic continuation and values at negative integers for Riemann's zeta function, Proc. Amer. Math. Soc., 81 (1981), no. 4, 513-517.
Z(427.30005),448.10032; M82e:10069; R1982,1B51

[4] Kummer and Herbrand criteria in the theory of function fields, Duke Math. J., 49 (1982), no. 2, 377-384.
Z(473.12013),485.12010; M83k:12012; R1983,2A275

[5] Units and class-groups in the arithmetic theory of function fields, Bull. Amer. Math. Soc. (N.S.), 13 (1985), no. 2, 131-132.
Z573.12003; M86j:11120; R1986,6A502

GOSSET Th.,
[1] Sylvester's theorem relating to Bernoullian numbers, Messeng. Math. (2), 40 (1911), 145-149.
J42.208

GOTO K.,
[1] A twisted adjoint $L$-value of an elliptic modular form, J. Number Theory 73 (1998), no. 1, 34-46.
Z924.11036; M99j:11052

GOULD H.W.,
[1] Generating functions for products of powers of Fibonacci numbers, Fibonacci Quart. 1 (1963), no. 2, 1-16.
Z147.02106; M33 #93

[2] Note on recurrence relations for Stirling numbers, Publ. Inst. Math. (Beograd) (N.S.), 6 (20) (1966), 115-119.
Z145,14; M34#4190; R1967,4V194

[3] Explicit formulas for Bernoulli numbers, Amer. Math. Monthly, 79 (1972), 44-51.
Z227.10010; M46#5229; R1972,7V249

[4] Bibliography of aritcles on the special number sequences of Bernoulli, Stirling, Euler, Worpitzky, etc., unpublished cardfile, 1971.

[5] Comment on Problem 67-5, "up-down" permutations, SIAM Review, 10 (1968), 225-226.

GOULD H.W., SQUIRE W.,
[1] Maclaurin's second formula and its generalization, Amer. Math. Monthly, 70 (1963), no. 1, 44-52.
Z116,92; M26#4073; R1963,12B27

GRAF J. H.,
[1] Praktische Integration von L. Schläfli, Mitt. der Naturforschenden Gesellschaft Bern, 1900.

GRAHAM R.L., KNUTH D.E., PATASHNIK O.,
[1] Concrete Mathematics. Addison-Wesley Publ. Co., Reading, MA, 1989. xiv + 625 pp.
Z668.00003; M91f:00001

GRANVILLE A.,
[1] On Krasner's criteria for the first case of Fermat's Last Theorem, Manuscr. Math., 56 (1986), no. 1, 67-70.
Z599.12013; M87i:11037; R1986,12A160

[2] The Kummer-Wieferich-Skula approach to the first case of Fermat's Last Theorem, In: F. Q. Gouvêa and N. Yui (Eds.), Advances in Number Theory (Proc., Third Conference of the Canadian Number Theory Assoc., Aug. 18-24, 1991, Queen's University at Kingston), 479-497 . Clarendon Press, Oxford, 1993.
Z790.11020; M96m:11020

[3] Arithmetic properties of binomial coefficients. I. Binomial coefficients modulo prime powers. Organic mathematics (Burnaby, BC, 1995), 253--276, CMS Conf. Proc., 20, Amer. Math. Soc., Providence, RI, 1997.
Z980.06321; M99h:11016

GRANVILLE A., MONAGAN M.B.,
[1] The first case of Fermat's last theorem is true for all prime exponents up to 714,591,416,091,389, Trans. Amer. Math. Soc., 306 (1988), no. 1, 329-359.
Z645.10018; M89g:11025; R1988,12A119

[2] The status of Fermat's last theorem - mid 1994. Maple Tech. Newsletter, special Issue, 1994, 2-9.

GRANVILLE A., SHANK H.S.,
[1] Defining Bernoulli polynomials in Z/pZ (a generic regularity condition), Proc. Amer. Math. Soc., 108 (1990), no. 3, 637-640.
Z645.10018; M90f:11015; R1990,12A92

GRANVILLE A., SUN ZHI-WEI,
[1] Values of Bernoulli polynomials. Pacific J. Math. 172 (1996), no. 1, 117-137.
Z856.11008; M98b:11018; R1997,11A142

GRANVILLE A.: see also ALMKVIST G., GRANVILLE A.

GRANVILLE A.: see also FUNG G., GRANVILLE A., WILLIAMS H.C.

GRAS G.,
[1] Classes d'idéaux des corps abéliens et nombres de Bernoulli généralisés, Ann. Inst. Fourier, 27 (1977), no. 1, 1-68.
Z(336.12004)343.12003; M56#8534; R1978,1A328

[2] Canonical divisibilities of values of p-adic L-functions, London Math. Soc., Lecture Notes Series, No. 56, (1982), 291-299.
Z494.12006; R1983,2A271

[3] Pseudo-mesures p-adiques associées aux fonctions L de Q, Manuscr. Math., 57 (1987), no. 4, 373-415.
Z658.12008(599.12016); M89d:11109; R1987,9A373

[4] Relations congruentielles linéaires entre nombres de classes de corps quadratiques, Acta Arith., 52 (1989), no. 2, 147-162.
Z618.12004; M90i:11127; R1990,1A332

[5] Sur la structure des groupes de classes relatives. Avex un appendice d'exemples numériques (par T. Berthier). Ann. Inst. Fourier, 43 (1993), no. 1, 1-20.
Z786.11065; M94i:11091

[6] Étude d'invariants relatifs aux groupes des classes des corps abéliens, Journées Arithmétiques de Caen (Univ. Caen, Caen, 1976), pp. 35-53. Asterisque No. 41-42, Soc. Math. France, Paris, 1977.
Z445.12002; M56 #5489

GRAS G., JAULENT J.-F.,
[1] Sur le corps de nombres réguliers, Math. Z., 202 (1989), no. 3, 343-365.
Z704.11040; M90i:11128

GRASSL R. M.,
[1] Euler numbers and skew-hooks, Math. Mag., 66 (1993), no. 3, 181-188.
Z801.05008; M94e:11016; R1996,6A76

GRAVE D.A.
[1] Elementarnyi kurs teorii chisel [Elementary handbook on number theory], 2nd edition. Kiev, (1913).
J44.207

GREENBERG R.,
[1] A generalization of Kummer's criterion, Invent. Math., 21 (1973), 247-254.
Z269.12005; M48#11056; R1974,3A268

[2] On p-adic L-functions and cyclotomic fields, Nagoya Math. J., 56 (1974), 61-77.
Z315.12008; M50#12984; R1975,9A297

[3] On the Jacobian variety of some algebraic curves, Compositio Math. 42 (1980/81), no. 3, 345-359.
Z475.14026; M82j:14036

GREENBERG R.: see also FERRERO B., GREENBERG R.

GREITHER C.,
[1] Class group of abelian fields, and the main conjecture, Ann. Inst. Fourier, 42 (1992), no. 3, 449-499.
Z729.11053; M93j:11071; R1993,5A335

GRENSING D., GRENSING G.,
[1] Generalized Campbell-Baker-Hausdorff formula, path-ordering and Bernoulli numbers. Z. Phys. C, 33 (1986), no. 2, 307-317.
M88c:22008; R1987,8B842

GRIGOREV E.I.,
[1] Bernullievy chisla vysshikh poryadkov [Bernoullian numbers of higher orders]. Izv. fiz.-mat. obshch. Kazansk. Univ. (2) 7(1898), 146-202.
J20.221

GROSJEAN C.C.,
[1] Approximations for the sum function of the Fourier series $\sum_{n=1}^\infty sin(nx)/n^2$, Simon Stevin, 39 (1966), 93-116.
Z241.65015; M33#5089; R1967,3B58

[2] An infinite set of recurrence formulae for the divisor sums. I, II, Bull. Soc. Math. Belg. Sér. A, 29 (1977), no. 1, 3-49; no. 2, 95-138.
Z442.10044; M83d:10005a,b

GROSS B.H.,
[1] On the Factorization of p-adic L-series, Invent. Math., 57 (1980), no. 1, 83-95.
Z472.12011; M82a:12010; R1980,9A339

[2] Arithmetic on elliptic curves with complex multiplication, Lecture Notes in Math., No. 776, Berlin, (1980), 95pp.
Z433.14032*; M81f:10041; R1981,2A432K

[3] Representation theory and the cuspidal group of $ X(p)$, Duke Math. J., 54 (1987), no. 1, 67-75.
Z629.14021; M89b:11052; R1987,11A546

[4] On the value of abelian L-functions at s=0, J. Fac. Sci. Univ. Tokyo, IA, 35 (1988), no. 1, 177-197.
Z681.12005; M89h:11071; R1988,10A317

GROSS B.H.: see also BUHLER J.P., GROSS B.H.

GROSSWALD E.,
[1] Comments on some formulae of Ramanujan, Acta Arith., 21 (1972), no. 1, 25-34.
Z246.10024; M46#1744; R1973,4A192

[2] Representations of integers as sums of squares, Springer-Verlag, New York-Berlin, 1985. xi+251 pp.
Z574.10045; M87g:11002; R1986,4A143K

[3] Die Werte der Riemannschen Zetafunktion an ungeraden Argumentstellen, Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. II, (1970), 9-13.
Z206,59; M42#7606; R1972,10A87

[4] Relations between the values of zeta and L-functions at integral arguments, Acta Arith., 24 (1973), 369-378.
Z242.12008; M48#11005

GROSSWALD E.: see also RADEMACHER H., GROSSWALD E.

GRUDER, O.,
[1] Über die Potenzsummen komplexer Zahlen und die entsprechende Bernoulli'sche Funktion, Sitzungsber. Kaiserl. Akad. der Wiss. Wien, Math.-naturw. Klasse, Abt. IIa, 125 (1916), no. 6, 613-657.
J46.359

[2] Über die Entwicklungskoeffizienten elliptischer Funktionen, Sitzungsber. Kaiserl. Akad. der Wiss. Wien, Math.- naturw. Klasse, Abt. IIa,, 126 (1917), 125-183.
J46.I.603

[3] Über teilerfremde Zahlen und deren Potenzsummen, Sitzungsber. Kaiserl. Akad. der Wiss. Wien, Abt. IIa, 137 (1928), 381-407.
J54.181

[4] Über symmetrische Grundfunktionen natürlicher Zahlen, J. Reine Angew. Math., 161 (1929), 152-178.
J55.I.94

GRÜN O.,
[1] Zur Fermatschen Vermutung, J. Reine Angew. Math., 170 (1934), 231-234.
J60.I.128; Z8,242

[2] Eine Kongruenz für Bernoullische Zahlen, Jahresber. Deutsch. Math.-Verein., 50 (1940), 111-112.
J66.139; Z23,203; M2-34d

[3] Beziehungen zwischen Bernoullischen Zahlen, Math. Ann., 135 (1958), 417-419.
Z102,50; M20#2478; R1959,4424

GRUNDMAN H.G.,
[1] The arithmetic genus of Hilbert modular varieties over non-Galois cubic fields, J. Number Theory, 37 (1991), no. 3, 343-365.
Z715.11023; M92d:11047

GRUNERT J.A.,
[1] "Bernoulli'sche Zahlen" in Supplemente zu Georg Simon Klügel's Wörterbuche, Erste Abtheilung. Leipzig, 1833.

GUARESCHI G.,
[1] Espressione dei numeri di Bernoulli mediante funzioni simmetriche complete, Boll. Mat., Genova (4), 1 (1940), 17-19.
J66.319; M2-88f

GUINAND A.P.,
[1] The umbral method: a survey of elementary mnemonic and manipulative uses, Amer. Math. Monthly, 86 (1979), no. 3, 187-195.
Z406.10013; M80e:05001; R1980,1V1291

GUNARATNE H.S.,
[1] A new generalisation of the Kummer congruence. In: Computational algebra and number theory (Sydney, 1992), 255-265. Math. Appl., 325, Kluwer Acad. Publ., Dordrecht, 1995.
Z833.11005; M96j:11148

[2] Periodicity of Kummer congruences. In: Number Teory (K. Dilcher, Ed.), Fourth Conference of the Canadian Number Theory Association (Halifax, July 2-8, 1994), CMS Conference Proceedings 15, 209-214. Amer. Math. Soc., Providence, 1995.
Z843.11012; M97b:11024; R1997,2A75

GUNDERSON N.G.,
[1] Derivation of Criteria for the First Case of Fermat's Last Theorem and the Combination of these Criteria to Produce a New Bound for the Exponent, Ph.D. Thesis, Cornell University, Ithaca, New York, 1948, 111 pp.

GÜNTHER S.,
[1] Von der expliziten Darstellung der regulären Determinanten aus Binomialkoeffizienten, Zeits. f. Math. u. Physik 24 (1879), 96-103

GUO D.R.: see WANG Z.X., GUO D.R.

GUO-NIN: see HAN, GUO-NIN

GUO LIZHOU: see ZHANG ZHIZHENG, GUO LIZHOU

GUPTA H.,
[1] Selected Topics in Number Theory, Abacus Press, Turnbridge Wells, Kent, England, 1980, 394pp.
Z425.10001; M81e:10002

[2] On the numbers of Ward and Bernoulli, Proc. Indian Acad. Sci. A, 3 (1936), 193-200.
J62.I.51; Z13.293

GUPTA S.: see PRABHAKAR T.R., GUPTA S.

GUT M.,
[1] Eulersche Zahlen und grosser Fermatscher Satz, Comm. Math. Helv., 24 (1950), 73-99.
Z37,166; M12-243d

[2] Eulersche Zahlen und Klassenzahl des Körpers der 4l-ten Einheitswurzeln, Comm. Math. Helv., 25 (1951), 43-63.
Z42,36; M12-806f

GUT M., STÜNZI M.,
[1] Kongruenzen zwischen Koeffizienten trigonometrischer Reihen und Klassenzahlen quadratisch imaginärer Körper, Comm. Math. Helv., 41 (1967), 287-302.
Z149,290; M36#2591; R1967,9A97

GYIRES B.,
[1] On a combinatorial identity, Publ. Math. Debrecen, 31 (1984), no. 3-4, 217-219.
Z567.10008; M86h:05010; R1986,1V719

GYÖRY K., TIJDEMAN R., VOORHOEVE M.,
[1] On the Diophantine equation $1^k+\cdots+x^k+R(x)=y^z$, Acta Math., 143 (1979), no. 1-2, 1-8.
Z426.10019; M80e:10020; R1980,3A84

[2] On the equation $1^k+\cdots+x^k=y^z$, Acta Arith., 37 (1980), 233-240.
Z(365.10014)439.10010; M82h:10021; R1981,6A104


HACHIMORI Y., ICHIMURA H.,
[1] Semi-local units modulo Gauss sums, Manuscripta Math. 95 (1998), no. 3, 377-395.
Z980.22003; M99h:11120

HADAMARD J.,
[1] Sur la série de Stirling, Proc. Fifth Intern. Congress Math., 1 (1913), 303-305.
J44.315

HAIGH C.W.,
[1] Newton's identities, generalised cycle-indices, universal Bernoulli numbers and truncated Schur-functions, J. Math. Chem. (to appear).

HALBRITTER U.,
[1] Eine elementare Methode zur Berechnung von Zetafunktionen reell-quadratischer Zahlkörper, Math. Ann., 271 (1985), no. 3, 359-379.
Z(541.12008), 556.12002; M86i:11067; R1986,2A460

[2] Berechnung der Werte von verallgemeinerten Zetafunktionen reell-quadratischer Zahlkörper mittels Dedekindscher Summen, J. Number Theory, 17 (1983), no. 3, 285-322.
Z522.12013; M85h:11072; R1984,5A115

[3] Anwendung einer Summationsformel auf Dirichletsche Reihen und verallgemeinerte Dedekindsche Summen, Acta Arith., 43 (1984), no. 4, 349-359.
Z(492.10008)534.10008; M86b:11032; R1985,1A167

[4] Some new reciprocity formulas for generalized Dedekind sums, Resultate Math. 8 (1985), no. 1, 21-46.
Z577.10011; M87a:11043

HALL R.R., WILSON J.C.,
[1] On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums. Math. Proc. Cambridge Philos. Soc., 114 (1993), no. 1, 9-24.
Z783.11021; M94c:11037

HALL R.R., WILSON J.C., ZAGIER D.,
[1] Reciprocity formulae for general Dedekind-Rademacher sums, Acta Arith., 73 (1995), no. 4, 389-396.
Z847.11020; M96j:11054; R1996,11A182

HALL T.G.,
[1] Art calcul of finite differences, Encycl. Pure Math., (1847), 261-270.

HAMILTON W.R.,
[1] On an expression for the numbers of Bernoulli, by means of a definite integral, and on some connected progresses of summation and integration, Phil. Mag., 23 (1843), 360-367.

HAMMOND J.,
[1] On the relation between Bernoulli's numbers and the binomial coefficients, Proc. London Math. Soc., 7 (1875), 9-14.
J8.144

HAN GUO-NIU,
[1] Calcul Denertien, Publ. Inst. Rech. Math. Avan., 1991, no. 476, 1-119.
M93h:05169; R1993,4A121

[2] Symétries trivariés sur les nombres de Genocchi. European J. Combin. 17 (1996), no. 4, 397--407.
Z852.0500; M97e:05015

HAN GUO-NIU, ZENG JIANG,
[1] On a $q$-sequence that generalizes the median Genocchi numbers. Ann. Sci. Math. Québec, 23 (1999), no. 1, 63-72.

HAN G.-N.; RANDRIANARIVONY A.; ZENG J.,
[1] Un autre $q$-analogue des nombres d'Euler. Sém. Lothar. Combin. 42 (1999), Art. B42e, 22 pp. (electronic).

HANSEN E.R.,
[1] A Table of Series and Products, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1975.

HAO F.H., PARRY C.J.,
[1] Generalized Bernoulli numbers and m-regular primes, Math. Comp., 43 (1984), no. 167, 273-288.
Z548.12006; M85h:11062; R1985,6A111

HARDER G.,
[1] Über spezielle Werte von L-Funktionen, Mitt. Math. Ges. Hamburg, 11 (1982), no. 1, 121-127.
Z503.12009; M84b:12019

HARDER G., PINK R.,
[1] Modular konstruierte unverzweigte abelsche $p$-Erweiterungen von $ Q(\zeta_p)$ und die Struktur ihrer Galoisgruppen. Math. Nachr., 159 (1992), 83-99.
Z773.11069; M95b:11100

HARDY G.H.,
[1] A formula of Ramanujan, J. London Math. Soc., 3 (1928), 238-240.

[2] Divergent Series. Oxford University Press, 1949. xvi + 396 pp.
Z32.058*; M11-25a

HARDY G.H., WRIGHT E.M.,
[1] An introduction to the theory of numbers, 5th Ed., Oxford Science Publications, 1979.
Z423.10001; M81i:10002; R1961,5A162K

HARE D.E.G.,
[1] Computing the principal branch of log-Gamma, J. Algorithms 25 (1997), no. 2, 221-236.
Z887.68055

HÄRKÖNEN K.,
[1] On the Diophantine equation $x^l+y^l=cz^l$ in the third case, Ann. Univ. Turku., Ser. A1, (1980), no. 180, 1-16.
M81m:10023; R1981,5A134

HARTREE D.R.,
[1] Numerical Analysis, Clarendon Press, Oxford, 1952. xiv +287 pp.
Z49,359; M14-690f; R1953,458PEII

HARTUNG P.: see CHOWLA S., HARTUNG P.

HARUKI H., RASSIAS T.M.,
[1] New integral representations for Bernoulli and Euler polynomials, J. Math. Anal. Appl., 175 (1993), no. 1, 81-90.
Z776.11009; M94e:39016

HASHIMOTO K., KOSEKI H.,
[1] Class numbers of definite unimodular Hermitian forms over the rings of imaginary quadratic fields, Tôhoku Math. J. (2), 41 (1989), no. 1, 1-30.
Z668.10029; M90g:11050; R1990,5A123

HASSE H.,
[1] Ein Summierungsverfahren für die Riemannsche $\xi$-Reihe, Math. Z., 32 (1930), 458-464.
J56.II.894

[2] Über die gewöhnlichen und verallgemeinerten Bernoullischen Zahlen, Simposio di Analisi, v. II, (1961), 67-72, "Archimedes Commemoration in 20th Century", Siracusa.
Z123,39; M30#4712

[3] Sulla generalizzazione di Leopoldt dei numeri di Bernoulli e sua applicazione alla divisibilità del numero della classi nei corpi numerici abeliani, Rend. Math. e Applic., 21 (1962), 9-27.
Z111,45; M25#3925; 25, p.1243; R1963,3A168

[4] Über die Bernoullischen Zahlen, Leopoldina, Reihe 3, 1962/63, 8/9 (1965), 159-167.
Z166,50; R1966,4A95

[5] Vandiver's congruence for the relative class-number of the p-th cyclotomic field, J. Math. Anal. Appl., 15 (1966), 87-90.
Z139,281; M33#4040; R1967,8A101

[6] Number Theory, Akademie-Verlag, Berlin, 1979. (A corrected and enlarged translation of Hasse, Zahlentheorie, 3rd Edition, Akademie-Verlag, Berlin, 1969.)
Z423.12001; M40#7185; R1970,2A305K

HATADA K.,
[1] On the values at rational integers of the p-adic Dirichlet L-functions, J. Math. Soc. Japan, 31 (1979), no. 1, 7-27.
Z399.12003; M80f:12010; R1979,9A334

[2] Mod 1 distribution of Fermat and Fibonacci quotients and values of zeta functions at $2-p$, Comment. Math. Univ. St. Paul., 36 (1987), no. 1, 41-51.
Z641.12008; M88i:11085; R1988,8A111

[3] Notes on Bernoulli numbers, Sci. Rep. Fac. Ed. Gifu Univ. Natur. Sci., 19 (1995), no. 2, 157-166.
Z825.11010; M96c:11024

HAUSS M.,
[1] Verallgemeinerte Stirling, Bernoulli und Euler Zahlen, deren Anwendungen und schnell konvergente Reihen f\"ur Zeta Funktionen. (German) [Generalized Stirling, Bernoulli and Euler numbers and their applications and fast convergent series for zeta functions] Dissertation, RWTH Aachen, Aachen, 1995. Berichte aus der Mathematik. [Reports from Mathematics] Verlag Shaker, Aachen, 1995. iv+209 pp.
Z867.11010; M97c:11029

[2] An Euler-Maclaurin-type formula involving conjugate Bernoulli polynomials and an application to $\zeta(2m+1)$. Commun. Appl. Anal. 1 (1997), no. 1, 15-32.
Z877.11009; M98b:11019

[3] A Boole-type formula involving conjugate Euler polynomials. Charlemagne and his heritage. 1200 years of civilization and science in Europe, Vol. 2 (Aachen, 1995), 361-375, Brepols, Turnhout, 1998.
M99k:11030

HAUSS M.: see BUTZER P.L., FLOCKE S., HAUSS M.

HAUSS M.: see BUTZER P.L. et al

HAUSSNER R.,
[1] Zur Theorie der Bernoull'ischen und Euler'schen Zahlen, Nachr. Kgl. Gesellsch. Wiss., Göttingen, 21 (1893), 777-809.
J25.414

[2] Independente Darstellung der Bernoull'ischen und Euler'schen Zahlen durch Determinanten, Zeitsch. für Math. und Phys., 39 (1894), 183-188.
J25.413

[3] Über verallgemeinerte Eulersche Zahlen und Tangentenkoeffizienten, Ber. über die Verhandl. der Königl. Sächs. Ges. der Wiss. Leipzig, Math.-phys. Kl., 62 (1910), 386-418.
J41.499

[4] Über verallgemeinte Tangenten- und Sekantenkoeffizienten, Arch. der Math. u. Phys. (3), 17 (1911), 333-337.
J42.208

HEASLET M.A.: see USPENSKY J.V., HEASLET M.A.

HEATH R.,
[1] Euler sums, Tech. Engng. News, 57 (1956), no. 5, 58-60.
R1957,2444

HEATH-BROWN D.R.: see ADLEMAN L.M., HEATH-BROWN D.R.

HENNEBERGER, M.,
[1] Beiträge zur Theorie der Integrale der Bernoullischen Funktionen, Dissertation, Universität Bern, 1901, 66p.
J(34.492)

HENSEL K.,
[1] Gedächtnisrede auf E.E. Kummer, Abhandl. zur Geschichte der Math. Wiss., Heft 29 (1910), 18-31.
J41.15

[2] E.E. Kummer und der grosse Fermatsche Satz, Reden Marburger Akad. No. 23, N.G. Elwertsche Verlagsbuchhandlung, 1910.
J41.16

HERBRAND J.,
[1] Sur les classes des corps circulaires, J. Math. Pures Appl. (9), 11 (1932), 417-441.
J58.I.180; Z6,008

HERGET W.,
[1] Bernoulli-Polynome in $Z_n$, Dissertation, TU Braunschweig, 1975.
Z359.10016*

[2] Minimum periods modulo $n$ for Bernoulli numbers, Fibonacci Quart., 16 (1978), no. 6, 544-548.
Z397.10007; M80f:10011

[3] Bernoulli-Polynome in den Restklassenringen $Z\sb{n}$, Glas. Mat., Ser. 3, 14 (34)(1979), no. 1, 27-33.
Z402.10008; M80j:10018; R1979,12A88

[4] Minimum periods modulo $n$ for Bernoulli polynomials, Fibonacci Quart., 20 (1982), 106-110.
Z482.10011; M84b:10018

HERGLOTZ G.,
[1] Über das quadratische Reziprozitätsgesetz in imaginären quadratischen Zahlkörpern, Ber. Verh. Sächs. Akad. Wiss. Leipzig, 73 (1921), 303-310.
J48.170

[2] Über die Entwicklungskoeffizienten der Weierstrasschen $\wp$-Funktionen, Ber. Verh. Sächs. Akad. Wiss. Leipzig, 74 (1922), 269-289.
J48.438

HERMES H.: see EBBINGHAUS H.-D. et al.

HERMITE CH.,
[1] Extrait d'une lettre à M. Borchardt (sur les nombres de Bernoulli), J. Reine Angew. Math., 81 (1876), 93-95.
J7.131

[2] Sur la formule de Maclaurin, J. Reine Angew. Math., 84 (1877), 64-70.
J9.182

[3] Extrait d'une lettre, Nouv. Corres. Math., 6 (1880), 121-122.

[4] Lettre à M. Borchardt sur la fonction de Jacob Bernoulli, J. Reine Angew. Math., 79 (1875), 339-344.
J7.159

[5] Remarque sur les nombres de Bernoulli et les nombres d'Euler, Sitz. Kgl. Böhmischen Gesells. Wiss., Prag, (1894), no. 37, 1-4.
J25.411

[6] Sur la fonction $\log \Gamma (x)$, J. Reine Angew. Math., 115 (1895), 201-208.
J26.474

[7] Sur les nombres de Bernoulli, Mathesis (2), 5 (1895), suppl. 2, 1-7.
J26.285

HERMITE CH.: see also SONIN N.YA., HERMITE CH.

HERSCHEL J.F.W.,
[1] On the development of exponential functions, together with several new theorems relating to finite differences, Trans. Phil. Soc., (1814), 440-468; (1816), 25-45.

[2] Collection of examples of the calculus of finite differences, Cambridge, 1820.

HIDA H.,
[1] A p-adic measure attached to the zeta functions associated with two elliptic modular forms. II. Ann. Inst. Fourier, 38 (1988), no. 3, 1-84.
Z645.10028; M89k:11120

[2] Elementary theory of $L$-functions and Eisenstein series. London Mathematical Society Student Texts, 26. Cambridge University Press, Cambridge, 1993. xii+386 pp.
M94j:11044

HIGGINS J.,
[1] Double series for the Bernoulli and Euler numbers, J. London Math. Soc., (2) 2 (1970), 722-726.
Z215,330; M43#147; R1972,2V304

HILBERT D.,
[1] Die Theorie der algebraischen Zahlkörper, Jahresber. Deutsch. Math.-Verein., 4 (1897), 175-546.
J28.157

HILL C.J.D.,
[1] När äro de $n$ forsta termerno af Bernoullis serie gifven funktion af den i den sista ingäende derivatan: Öfversigt Kgl. Vetens.-Akad. Förhandl., Stockholm, 14 (1857), (1858), 259-261.

HINDENBURG C.F.,
[1] Sammlung combinatorisch-analytischer Abhandlungen, 2-te Sammlung, Leipzig, 1800, S. 337.

HIRZEBRUCH F.: see EBBINGHAUS H.-D. et al.

HLAWKA E., SCHOISSENGEIER J., TASCHNER R.,
[1] Geometric and Analytic Number Theory, Springer-Verlag, Berlin etc., 1991, x+238 pp..
Z749.11001; M92f:11002

HOFFMAN M. E.,
[1] Multiple harmonic series, Pacific J. Math., 152 (1992), no. 2, 275-290.
Z763.11037; M92i:11089; R1993,1A103

[2] Derivative polynomials for tangent and secant, Amer. Math. Monthly 102 (1995), no. 1, 23-30.
Z834.26002; M95m:26003

[3] Derivative polynomials, Euler polynomials, and associated integer sequences, Electron. J. Combin. 6 (1999), no. 1, Research Paper 21, 13 pp. (electronic)
M 2000c:11027

HOFSTETTER, P.,
[1] Die Bernoullische Funktion und die Gammafunktion, Dissertation, Universität Bern. Wälchli, Bern, 1912, 76p.
J(43.534)

HOGGATT V.E.: see ARKIN J., HOGGATT V.E.

HOLVORCEM P. R.,
[1] Laurent expansions for certain functions defined by Dirichlet series, Aequationes Math., 45 (1993), no. 1, 62-69.
Z770.30004; M93k:30005

HOLZAPFEL R.-P.,
[1] Zeta dimension formula for Picard modular cusp forms of neat natural congruence subgroups, Abh. Math. Sem. Univ. Hamburg 68 (1998), 169-192.

HONG SHAOFANG,
[1] Notes on Glaisher's congruences, Chinese Ann. Math. Ser. B 21 (2000), no. 1, 33-38.

HORADAM A. F.,
[1] Genocchi Polynomials, Proc. of the Fourth International Conference on Fibonacci Numbers and Their Applications. Kluwer, Dordrecht, 1991, 145-166.
Z749.11019; M93i:11027

[2] Negative Order Genocchi Polynomials, Fibonacci Quart., 30 (1992), no. 1, 21-34.
Z749.11020; M93a:11016

[3] Generation of Genocchi polynomials of first order by recurrence relations, Fibonacci Quart., 30 (1992), no. 3, 239-243.
Z770.11015; M94e:05012

HORADAM A.F., SHANNON A.G.,
[1] Ward's Staudt-Clausen problem, Math. Scand., 39 (1976), no. 2, 239-250 (1977).
Z347.10010; M56#5411; R1978,5A78

HORADAM A.F.: see also MAHON BR. J.M., HORADAM A.F.

HORATA K.,
[1] An explicit formula for Bernoulli numbers, Rep. Fac. Sci. Technol., Meijo Univ., 29 (1989), no. 1, 1-6.
Z671.10008

[2] On congruences involving Bernoulli numbers and irregular primes, I. Rep. Fac. Sci. Technol., Meijo Univ., 30 (1990), 1-9.
R1991,2A167

[3] On congruences involving Bernoulli numbers and irregular primes, II. Rep. Fac. Sci. Technol., Meijo Univ., 31 (1991), 1-8.
Z856.11009; R1991,12A72

[4] On congruences involving Bernoulli numbers and irregular primes. III. Rep. Fac. Sci. Technol., Meijo Univ., 32 (1992), 15-22.
Z856.11010; R1993,5A168

HORNER J.,
[1] On the forms of $\Delta^{n}0^x$ and their congeners, Quart. J. Math., 4 (1861), 111-123; 204-220.

HOFSTETTER P.,
[1] Die Bernoullische Funktion und die Gammafunktion, Dissertation, Bern, 1911, 108 pp.
J43.534

HOWARD F.T.,
[1] A sequence of numbers related to the exponential function, Duke Math. J., 34 (1967), 599-615.
Z189,42; M36#130; R1968,6V312

[2] Some sequences of rational numbers related to the exponential function, Duke Math. J., 34 (1967), 701-716.
Z189,42; M36#131

[3] Properties of the van der Pol Numbers and polynomials, J. Reine Angew. Math., 260 (1973), 35-46.
Z254.10013; M47#6603

[4] Roots of the Euler polynomials, Pacific J. Math., 64 (1976), no. 1, 181-191.
Z331.10005; M54#5444; R1977,4V445

[5] Numbers generated by the reciprocal of $e^x-x-1$, Math. Comp., 31 (1977), no. 138, 581-598.
Z351.10010; M55#12627

[6] A theorem relating potential and Bell polynomials, Discrete Math., 39 (1982), no. 2, 129-143.
Z478.05008; M84e:05015; R1982,10V455

[7] Integers related to the Bessel Function $J_1(z)$, Fibonacci Quart., 23 (1985), no. 3, 249-259.
Z578.10016; M88b:11010; R1986,4A111

[8] Extensions of congruences of Glaisher and Nielsen concerning Stirling numbers, Fibonacci Quart., 28 (1990), no. 4, 355-362.
Z726.11012; M92i:11028; R1991,8V320

[9] The van der Pol numbers and a related sequence of rational numbers, Math. Nachr., 42 (1969), 89-102.
Z208.05401; M41#3385

[10] Generalized van der Pol numbers, Math. Nachr., 44 (1970), 181-191.
Z194.07302; M45#8600

[11] Polynomials related to the Bessel functions, Trans. Amer. Math. Soc., 210 (1975), 233-248.
Z308.10008; M52#253; R1976,4B45

[12] Factors and roots of the van der Pol polynomials, Proc. Amer. Math. Soc., 53 (1975), no. 1, 1-8.
Z313.10011; M52#252; R1976,7V375

[13] A special class of Bell polynomials, Math. Comp., 35 (1980), no. 151, 977-989 .
Z 438.10012; M82g:10028; R1981,4V377

[14] Nörlund's number $B_n^{(n)}$. Applications of Fibonacci Numbers, Vol. 5 (G. E. Bergum et al., Eds.), 355-366, Kluwer Acad. Publ., Dordrecht, 1993.
Z805.11023; M95e:11029

[15] Congruences and recurrences for Bernoulli numbers of higher order. Fibonacci Quart., 32 (1994), no. 4, 316-328.
Z820.11009; M95k:11021

[16] Applications of a recurrence for Bernoulli numbers, J. Number Theory, 52 (1995), no. 1, 157-172.
Z805.11023; M96e:11027

[17] Formulas of Ramanujan involving Lucas numbers, Pell numbers, and Bernoulli numbers. In: G.E. Bergum et al. (eds.), Applications of Fibonacci Numbers, Vol. 6, 257-270. Kluwer Acad. Publ., Dordrecht, 1969.
Z852.11007; M97d:11039

[18] Explicit formulas for degenerate Bernoulli numbers, Discrete Math., 162 (1996), no. 1-3, 175-185.
Z873.11016; M97m:11024

[19] Sums of powers of integers via generating functions, Fibonacci Quart., 34 (1996), no. 3, 244-256.
Z859.11016; M98a:11025; R1997,10A200

[20] Lacunary recurrences for sums of powers of integers, Fibonacci Quart., 36 (1998), no. 5, 435-442

HSU L. C. [XU LI ZHI],
[1] Power-type generating functions. Approximation theory (Kecskemét, 1990), 405-412. Colloq. Math. Soc. János Bolyai, 58, North-Holland, Amsterdam, 1991.
Z768.41030; M94g:41054

[2] Finding some strange identities via Faa di Bruno's formula, J. Math. Res. Exposition 13 (1993), no. 2, 159-165.
Z783.05006; M94f:05007

HSU L.C., CHU W.,
[1] A kind of asymptotic expansion using partitions. Tôhoku Math. J., 43 (1991), no.2, 235-242.
Z747.41030; M92g:41038

HUANG I-CHIAU, HUANG SU-YUN,
[1] Bernoulli numbers and polynomials via residues, J. Number Theory, 76 (1999), no. 2, 178-193.
M2000d:11027

HURWITZ A.,
[1] Einige Eigenschaften der Dirichlet'schen Functionen $\Gamma (s) = \sum (D/n){1/n^s}$, die bei der Bestimmung der Classenzahlen binärer quadratischer Formen auftreten, Zeitsch. für Math. und Physik, 27 (1882), no. 1, 86-101.
J14.371

[2] Über die Anzahl der Klassen binärer quadratischer Formen von negativer Determinante, Acta Math., 19 (1895), 351-384.
J26.226

[3] Über die Entwicklungscoefficienten der lemniscatischen Functionen, Math. Ann., 51 (1898), 196-226.
J29.385

[4] Über die Entwickelungscoefficienten der lemniskatischen Functionen. Nachr. Kgl. Ges. Wiss. Göttingen, (1897), 273-276.
J28.393

HUSSAIN M.A., SINGH S.N.,
[1] On generalized polynomial set $D_n(x;a,k)$, Indian J. Pure Appl. Math., 9 (1978), no. 11, 1158-1162.
Z402.33007; M80b:10018; R1979,4B52

HUTCHINSON J.I.,
[1] On the roots of the Riemann zeta function, Trans. Amer. Math. Soc., 27 (1925), 49-60.
J51.267,271


IBRAHIMOGLU I.,
[1] A proof of Stickelberger's theorem (Stickelberger teoremi'nin bir ispat{\=i),Hecettepe Bull. Natur. Sci. and Eng. 12 (1983), 279-287.
Z565.12004; R1984,5A124

[2] The value of the Dirichlet L-functions at negative integral points, Hacettepe Bull. Natur. Sci. and Eng., 13 (1984), 63-67.
Z565.10035; R1985,3A124

[3] (C,k)-summability of the Dirichlet L-functions, Hacettepe Bull. Natur. Sci. and Eng., 13 (1984), 59-62.
Z565.10034; R1985,3B86

IBUKIYAMA T.,
[1] On some elementary character sums, Comment. Math. Univ. St. Paul. 47 (1998), no. 1, 7-13.
Z921.11046; M99h:11094

IBUKIYAMA T., SAITO H.,
[1] On $L$-functions of ternary zero forms and exponential sums of Lee and Weintraub. J. Number Theory, 48 (1994), no. 2, 252-257.
Z824.11033; M95i:11032

[2] On zeta functions associated to symmetric matrices, I: An explicit form of zeta functions, Amer. J. Math., 117 (1995), no. 5, 1097-1155.
Z846.11028; M96j:11120

ICHIMURA H.: see HACHIMORI Y., ICHIMURA H.

IKEDA M.,
[1] Some inequalities for Bernoulli's polynomials and related functions, Monatsh. Math., 68 (1964), 224-234.
Z129.284; M31#2435; err.31, p.1336; R1965,3B71

IMAI H.,
[1] Values of $p$-adic $L$-functions at positive integers and $p$-adic log multiple gamma functions. Tôhoku Math. J., 45 (1993), no. 4, 505-510.
Z809.11067; M95c:11139; R1994,8A371

IMAMOGLU Ö.: see DUKE W., IMAMOGLU Ö.

IMAOKA M.,
[1] Generalized Bernoulli numbers on the $K{\rm O}$-theory. Hiroshima Math. J. 26 (1996), no. 1, 181-188.
Z865.55003; M97c:55016

IMSHENETSKII V.G.,
[1] O funktsiyakh Yakova Bernulli i vyrazhenii raznosti mezhdu odnopredel'nymi summoyu i integralom [On functions of Jacob Bernoulli and an expression for the difference between sum and integral with the same limits]. Uch. zap. Kazansk. Univ. 6 (1870), 244-265.
J2.124

[2] Ob odnom obobshchenii funktsii Yakova Bernulli [On a generalization of the function of Jacob Bernoulli]. Zap. Peterb. Akad. Nauk, (7), 31 (1883), no.II, 1-58.
J15.370

[3] O nekotorykh prilozheniyakh obshchikh funktsii Bernulli, Prilozhenie No. 2 [On some applications of general functions of Bernoulli]. Prilozhenie No. 2 k zap. Peterb. Akad. Nauk 52 (1886), 1-62.
J18.373

INKERI K.,
[1] On the second case of Fermat's last theorem, Ann. Acad. Sci. Fenn., Ser. AI, Math.-Phys. Kl., (1949), no. 60, 1-32.
Z33,351; M11-500d

[2] Über die Klassenzahl des Kreiskörpers der $l$-ten Einheitswurzeln, Ann. Acad. Sci. Fenn., Ser. AI, (1955), no. 199, 1-12.
Z65,269; M18-20d; R1956,7084

[3] The real roots of Bernoulli polynomials, Turun Yliopiston Julkais., (Annales Universitatis Turkuensis), 1959, Ser. AI, no. 37, 1-20.
Z104,15; M22#1703; R1961,5B376

INVERNIZZI S.,
[1] On the periodic BVP for the forced Duffing equation, Rend. Inst. Mat. Univ. Trieste, 19 (1987), no. 1, 64-75.
Z651.34066; M89f:34026; R1988,10B1160

IRELAND K., ROSEN M.,
[1] A classical introduction to modern number theory, Springer-Verlag, New York, 1982.
Z482.10001*; M83g:12001; R1983,1A63K

IRELAND K., SMALL, D.,
[1] A note on Bernoulli-Goss polynomials, Can. Math. Bull., 27 (1984), no. 2, 179-184.
Z531.12012; M85f:11093; R1985,1A212

ISEKI S.,
[1] The transformation formula for the Dedekind modular function and related functional equation, Duke Math. J., 24 (1957), 653-662.
Z93.259; M19-943a; R1959,1222

ISHIBASHI M.,
[1] On a proof of the Artin-Hasse formula for the norm residue symbol, Mem. Fac. Sci. Kyushu Univ. Ser. A, 39 (1985), no. 1, 95-103.
Z547.12004; M86g:11069; R1985,12A332

[2] An elementary proof of the generalized Eisenstein formula, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 197 (1988), no. 8-10, 443-447.
Z684.10014; M91k:11075

[3] The value of the Estermann zeta functions at $s=0$. Acta Arith. 73 (1995), no. 4, 357-361.
Z845.11034; M96k:11109; R1997,10A143

[4] $\bold Q$-linear relations of special values of the Estermann zeta function, Acta Arith. 86 (1998), no. 3, 239-244.

ISHIBASHI M., KANEMITSU S.,
[1] Fractional part sums and divisor functions, I. In: Number Theory and Combinatorics, Japan 1984. World Sci Publ., Philadelphia, 1985, viii + 446 pp.
Z601.o10032; M87e:11093

ISHIBASHI M., SHIRATANI K.,
[1] On explicit formulas for the norm residue symbol in prime cyclotomic fields, Mem. Fac. Sci., Kyushu Univ., Ser. A, 38 (1984), no. 2, 201-231.
Z595.12008; M85j:11169; R1985,6A297

ISMAIL M.E.H., STEWART D.,
[1] On Dumont's polynomials, Discrete Math. 41 (1982), no. 2, 155-160.
Z492.05004; M83m:10010; R1983,2V458

ISMAIL M.E.H.: see also GOSPER R.W., ISMAIL M.E.H., ZHANG R.

ISRAILOV M.I.,
[1] The reconstruction of functions given by their moments, by means of Bernoulli polynomials. Dokl. Akad. Nauk USSR, 1967, no. 10, 7-10.
Z202,124; M46#5923; R1968,9B4

[2] On the Laurent expansion of the Riemann zeta function. (Russian), Trudy Mat. Inst. Steklov., 158 (1981), 98-104. Engl. transl.: Proc. Steklov Inst. Math. 1983, no. 4, 105-112.
Z477.10031; M83m:10069; R1982,5B39

ITZYKSON C.: see WALDSCHMIDT M. et al.

IVIC A.,
[1] Topics in recent zeta function theory, Publ. Math. D'Orsay, (1983).
Z534.10032*; M86b:11055

[2] The Riemann zeta-function: The theory of the Riemann zeta-function with applications. John Wiley & Sons, New York etc., 1985, xvi + 517 pp.
Z556.10026; M87d:11062; R1985,11A132K

IVIC A., TE RIELE H.J.J.,
[1] On the zeros of the error term for the mean square of $|\zeta({1\over 2}+it)|$. Math. Comp., 56 (1991), no.193, 303-328.
Z714.11051; M91e:11095

IWANIEC H.,
[1] Topics in classical automorphic forms. Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI, 1997. xii+259 pp. ISBN 0-8218-0777-3.
Z905.11023; M98e:11051

IWASAWA K.,
[1] On some invariants of cyclotomic fields, Amer. J. Math., 80 (1958), no. 3, 773-783; erratum, 81 (1959), no. 1, 280.
Z84,41; M23#A1631; R1961,5A247

[2] On p-adic L-functions, Ann. Math., 89 (1969), 198-205.
M42#4522; R1971,2A300

[3] Lectures on p-adic L-functions, Ann. of Math. Studies, Princeton, 1972, No. 74.
Z236.12001*; M50#12974; R1973,2A327

IWATA G.,
[1] A generalization of the Euler-Maclaurin sum formula, Natur. Sci. Rep. Ochanomizu Univ., 27 (1976), no. 1, 27-31.
Z351.33009; M54#14305; R1977,1B26


JACOBI C.G.J.,
[1] De usu legitimo formulae summatoriae Maclaurinianae, J. Reine Angew. Math., 12 (1834), 263-272.

JACOBSTHAL E.,
[1] Über eine Formel von Frobenius, Kgl. Norske Videns. Selsk. Forh. Trondheim, 22 (1950), 51-55.
Z36,012; M11-653e

[2] Zur Theorie der Bernoullischen Zahlen, Norske Vid. Selsk. Forh. Trondheim, 22 (1950), no. 24, 107-112.
Z36,012; M11-581b

[3] Number-theoretical propeties of binomial coefficients (Norwegian), Norske Vid. Selsk. Skr., Trondhjem, 1942, no. 4, 28pp. (1945).
M8-314d

JACOBSTHAL E.: see also BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.

JAKUBEC S.,
[1] On Vandiver's conjecture, Abh. Math. Sem. Univ. Hamburg, 64 (1994), 105-124.
Z828.11050; M95h:11116

[2] On divisibility of the class number of real octic fields of a prime conductor $p=n^4+16$ by $p$. Arch. Math. (Brno), 30 (1994), no. 4, 263-270.
Z818.11042; M96a:11120

[3] On the divisibility of $h\sp +$ by the prime $3$. Rocky Mountain J. Math. 24 (1994), no. 4, 1467-1473.
Z821.11053; M95m:11119

[4] Congruence of Ankeny-Artin-Chowla type for cyclic fields of prime degree $l$. Math. Proc. Cambridge Philos. Soc., 119 (1996), no. 1, 17-22.
Z853.11085; M96j:11145

[5] Congruence of Ankeny-Artin-Chowla type modulo $p\sp 2$ for cyclic fields of prime degree $l$. Acta Arith. 74 (1996), no. 4, 293-310.
Z853.11086; M97h:11135

[6] Connection between congruences $n\sp {q-1}\equiv 1\pmod {q\sp 2}$ and divisibility of $h\sp +$, Abh. Math. Sem. Univ. Hamburg, 66 (1996), 151-158.
Z; M98a:11145

[7] On divisibility of the class number $h\sp +$ of the real cyclotomic fields of prime degree $l$. Math. Comp. 67 (1998), no. 221, 369-398.
Z914.11057; M98d:11136

[8] Note on Wieferich's congruence for primes $p \equiv 1 \pmod{4}$, Abh. Math. Sem. Univ. Hamburg, 68 (1998), 193-197.
M99i:11012

[9] Note on the congruence of Ankeny-Artin-Chowla type modulo $p\sp 2$, Acta Arith. 85 (1998), no. 4, 377-388.
Z912.11041; M99m:11128

JAKUBEC S., LASSÁK M.,
[1] Congruence of Ankeny-Artin-Chowla type modulo $p\sp 2$. Number theory (Cieszyn, 1998). Ann. Math. Sil. No. 12, (1998), 75-91.
Z923.11154; M99m:11127

JAMES R. D.,
[1] On the expansion coefficients of the functions $u/sn\;u$ and $u^2/sn^2u$. Bull. Amer. Math. Soc., 40 (1934), 632-640.
J60.II.1056; Z9.400

JAMIESON A.M.,
[1] An expression for Bernoulli numbers, Proc. Glasgow Math. Assoc., 1 (1953), 126-128.
Z53,231; M15-289g

JANKOVIC Z.,
[1] Une démonstration de la formule de Bernoulli. (Serbo-Croatian. French summary.), Glasnik Mat.-Fiz. Astr. Ser. II, 7 (1952), 23-29.
Z82,17; M13-913a

[2] Two recurrence formulae for the sums $s_{2k}$. Hrvatsko Prirodoslovno Drustvo. Glasnik Mat.-Fiz. Astr. Ser. II., 8 (1953), 27-29.
Z53.39; M14-974b

JAPIC R.R., MITROVIC Z.M.,
[1] Bernoulli and Euler polynomials in k variables, Univ. Beograd. Publ. Elektrotechn. Fak. Ser. Math. Fiz., No. 412-460 (1973), 75-78.
Z274.33012; M48#6478; R1974,4V257

JAULENT J.-F.: see GRAS G., JAULENT J.-F.

JEFFERY H.M.,
[1] On Staudt's proposition relating to the Bernouillian numbers, Quart. J. Math., 6 (1864), 179-180.

JENSEN K.L.,
[1] Om talteoretiske Egenskaber ved de Bernoulliske Tal, Nyt Tidskr. f. Math., 26 (1915), 73-83.
J45.1257

[2] Note sur la congruence de Kummer relative aux nombres de Bernoulli, Overs. Danske Vidensk. Selsk. Forh., (1915), 321-331.
J45.304

JETTER K.,
[1] The Bernoulli spline and approximation by trigonometric blending polynomials, Resultate Math., 16 (1989), no. 3-4, 243-252.
Z682.42001; M91a:41009; R1990,4B109

JHA V.,
[1] Faster computation of irregular pairs corresponding to an odd prime. J. Indian Math. Soc., 59 (1993), no. 1-4, 149-152.
Z865.11088; M95d:11173

[2] The Stickelberger Ideal in the Spirit of Kummer with Appllication to the First Case of Fermat's Last Theorem. Queen's Papers in Pure and Applied Mathematics, No. 93. Kingston, Ontario 1993. xiv + 181 pp.
Z779.11057; M95d:11148

[3] On Krasner's theorem for the first case of Fermat's last theorem, Colloq. Math., 67 (1994), no. 1, 25-31.
Z813.11009; M95h:11025

JIANG ZENG: see RANDRIANARIVONY A., JIANG ZENG

JIN JINGYU: see ZHANG ZHIZHENG, JIN JINGYU

JOCHNOWITZ N.,
[1] A $p$-adic conjecture about derivatives of $L$-series attached to modular forms. $p$-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), 239--263, Contemp. Math., 165, Amer. Math. Soc., Providence, RI, 1994.
Z869.11040; M95g:11037

JOFFE S.A.,
[1] Sums of like powers of natural numbers. Quart. J. Math., 46 (1915), 33-51.
J45.1244

[2] Calculation of the first thirty-two Eulerian numbers from the central differences of zero. Quart. J. Pure Appl. Math., 47 (1916), 103-126.
J46.360

[3] Calculation of Eulerian numbers from central differences of zero. (Abstract) Bull. Amer. Math. Soc., 22 (1916), 381.
J46.360

[4] Calculation of eighteen more, fifty in all, Eulerian numbers from central differences of zero, Quart. J. Pure Appl. Math., 48 (1919), 193-271.

JOHNSEN J.,
[1] On the distribution of irregular primes, J. Number Theory, 8 (1976), no. 4, 434-437.
Z339.10012; M55#5552; R1977,5A60

JOHNSON W.,
[1] On the vanishing of the Iwasawa invariant $\mu_p$ for $p < 8000$, Math. Comp., 27 (1973), 387-396.
Z281.12006; M52#5621; R1974,1A355

[2] Irregular prime divisors of the Bernoulli numbers, Math. Comp., 28 (1974), no. 126, 653-657.
Z293.10008; M50#229; R1974,12A129

[3] Irregular primes and cyclotomic invariants, Math. Comp., 29 (1975), no. 129, 113-120.
Z302.10020; M51#12781; R1975,12A160

[4] On the distribution of quadratic residues (Abstract), Notices Amer. Math. Soc., 22 (1975), no. 1, A66.

[5] p-adic proofs of congruences for the Bernoulli numbers, J. Number Theory, 7 (1975), no. 2, 251-265.
Z308.10006; M51#12687; R1975,12A117

JOHNSONBAUGH R.,
[1] Summing an alternating series, Amer. Math. Monthly, 86 (1979), no. 8, 637-648.
Z425.65002; M80g:40003; R1980,8B19

JOLY J.-R.,
[1] Calcul des nombres de Bernoulli modulo $p^m$. Application à l'étude des nombers premiers irreguliers. Sémin. Théor. Nombres, Univ. Grenoble I, (1980-1981). Exposé No.4, (1981), 19pp.
Z475.10013

[2] Analyse numérique p-adique des nombres de Bernoulli et des séries $L$ de Dirichlet. Sémin. Théor. Nombres, Univ. Grenoble I, (1981-82). Exposé No.6, (1982), 14pp.
Z506.10010

[3] Calcul des nombres de Bernoulli modulo $p^m$, Sémin. Théor. Nombres, Paris, (1981-82),113-124. Sémin. Delange-Pisot-Poitou, Progr. Math., 38, Birkhäuser, Boston, Mass., 1983.
Z536.10011; M85g:10023; R1984,8A101

JONQUIERE A.,
[1] Note sur la série $\sum_{n=1}^{n=\infty}{{x^n}\over{n^s}}$. Bull. Soc. Math. France, 17 (1889), no.5, 142-152.
J21.246

[2] Note sur la série $\sum_{n=1}^{n=\infty}{{x^n}\over{n^s}}$. Översigt Kongl. Vet.-Akad. Förhandl., 5 (1889), 257-268.
J21.247

[3] Über eine Verallgemeinerung der Bernoulli'schen Funktionen und ihren Zusammenhang mit der verallgemeinerten Riemann'schen Reihe. Bihang K. Svenska Vet.-Akad. Handl., 16 (1891), no. 6, 1-28.
J23.432

JORDAN CH.,
[1] Calculus of finite differences, 2nd ed., Chelsea Publ. Co., New York, 1950, xxi +652 pp.
Z41,54; M1-74e

[2] Sur des polynomes analogues aux polynomes de Bernoulli et sur des formules de sommation analogues à celle de Maclaurin-Euler. Acta Scientiarum Math.(Szeged), 4 (1929), 130-150.
J55.266

JOSHI J.M.C.: see SRIVASTAVA H.M., JOSHI J.M.C., BISHT C.S.

JUNG W.,
[1] Poznamka k cislum Bernoulliho [A note on Bernoulli numbers], Casopis Pest. Mat. Fyz., 9 (1880), 103-108.
J12.195


KAIRIES H.H.,
[1] Definitionen der Bernoulli-Polynome mit Hilfe ihrer Multiplikationstheoreme, Manuscr. Math., 8 (1973), 363-369.
Z248.39003; M48#2057; R1973,8V304

KAIRIES H.H.: see also DICKEY L.J., KAIRIES H.H., SHANK H.S.

Z626.10012; M88g:05018

KALLIES J.,
[1] Verallgemeinerte Dedekindsche Summen und ein Gitterpunktproblem im n-dimensionalen Raum, J. Reine Angew. Math., 344 (1983), 22-37.
Z508.10007; M86d:11004; R1984,1A98

[2] Ein Beitrag zur Arithmetik der Bernoullischen Zahlen imaginär-quadratischer Zahlkörper, J. Reine Angew. Math., 361 (1985), 73-94.
Z561.12001; M87g:11031; R1986,4A399

KALLIES J., SNYDER C.,
[1] On the values of partial zeta functions of real quadratic fields at nonpositive integers, Math. Nachr., 175 (1995), 159-191.
Z856.11053; M96k:11137

KALYUZHNYI V.N.,
[1] A $p$-adic analogue of the Hurwitz zeta function.(Russian) Teor. Funktsii Funktsional. Anal. i Prilozhen., no. 40 (1983), 74-79.
Z555.12007; M85h:11078; R1984,2A321

[2] The power moment problem on a $p$-adic disk. Teor. Funktsii Funktsional. Anal. i Prilozhen., no. 39 (1983), 56-61.
Z561.12005; M85b:11077; R1984,1B135

[3] On certain sums with Stirling and Bernoulli numbers. (Russian) Vestnik Kharkov. Gos. Univ., no. 286 (1986), 87-94.
Z626.10012; M88g:05018

KAMIENNY S.,
[1] Modular curves and unramified extensions of number fields, Compositio Math., 47 (1982), no. 2, 223-225.
Z501.12011; M84e:12011; R1983,4A370

[2] Points of order $p$ on elliptic curves over $ Q(\sqrt p)$, Math. Ann., 262 (1982), no. 4, 413-424.
Z489.14010; M84g:14047; R1983,5A390

[3] Rational points on modular curves and abelian varieties, J. Reine Angew. Math., 359 (1985), 174-187.
Z569.14002; M86j:11061; R1986,4A589

[4] p-torsion in elliptic curves over subfields of $ Q(\mu_p)$, Math. Ann., 280 (1988), no. 3, 513-519.
Z626.14024; M90a:11061

[5] On $J_1(p)$ and the kernel of the Eisenstein ideal, J. Reine Angew. Math., 404 (1990), 203-208.
Z705.14025; M90m:11171; R1990,9A341

KAMIENNY S., STEVENS G.,
[1] Special values of L-functions attached to $X_1(N)$, Composito Math., 49 (1983), no. 1, 121-142.
Z519.14018; M84g:14021; R1983,11A588

KANEKO M.,
[1] A recurrence formula for the Bernoulli numbers, Proc. Japan Acad. Ser. A, 71 (1995), 192-193.
Z854.11012; M96i:11022; R1996,4V266

[2] Poly-Bernoulli numbers, J. Théor. Nombres Bordeaux 9 (1997), no. 1, 221-228.
Z887.11011; M98k:11013; R1998,4A85

[3] Multiple zeta values and poly-Bernoulli numbers (Japanese), Seminar Reports of the Department of Mathematics, Tokyo Metropolitan University, 1997, 42 pp.

KANEKO M.: see also ARAKAWA T., KANEKO M.,

KANELLOS S.G.,
[1] On Bernoulli's numbers, Bull. Soc. Math. Grèce, 28 (1954); 101-106. (Greek, English summary.)
Z57,10; M15-855d; R1956,2755

KANEMITSU S.,
[1] On some bounds for values of Dirichlet's L-function $L(s, \chi)$ at the point $s=1$, Mem. Fac. Sci. Kyushu Univ., Ser. A, 31 (1977), no. 1, 15-23.
Z351.10024; M55#12655; R1977,12A103

[2] Omega theorems for divisor functions, Tokyo J. Math., 7 (1984), no. 2, 399-419.
Z556.10031; M87c:11085; R1985,10A141

KANEMITSU S., KUZUMAKI T.,
[1] On a generalization of the Maillet determinant. Number theory (Eger, 1996), 271-287, de Gruyter, Berlin, 1998.
Z920.11071; M99h:11122

KANEMITSU S., SHIRATANI K.,
[1] An application of the Bernoulli functions to character sums, Mem. Fac. Sci. Kyushu Univ., Ser. A, 30 (1976), no. 1, 65-73.
Z336.10031; M54#249; R1976,9A151

[2] Applications of Bernoulli functions to Dirichlet character sums. (Japanese). Characteristics of arithmetic functions (Proc. Sympos., Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1975). Sûrikaisekikenkyûsho Kókyûroku, No. 274, (1976), 148-151.
Z336.10033; M56#15578

KANEMITSU S., SITARAMACHANDRA RAO R.,
[1] On a conjecture of P. Chowla and of S. Chowla and H. Walum, I, J. Number Theory, 20 (1985), no. 3, 255-261.
Z(467.10031)573.10036; M87d:11072a; R1986,1A110

[2] On a conjecture of S. Chowla and Walum, II, J. Number Theory, 20 (1985), no. 2, 103-120.
Z(467.10032)573.10037; M87d:11072b; R1986,1A111

KANEMITSU S.: see also ISHIBASHI M., KANEMITSU S.

KANO H.,
[1] On the equation $s(1^k+s^k+ \cdots +x^k)+r = by^z$, Tokyo J. Math., 13 (1990), no. 2, 441-448.
Z722.11022; M91m:11022; R1991,9A121

KAPTEYN J.C., KAPTEYN W.,
[1] Die Höheren Sinus. Sitzungsber. d. Kais. Akad. d. Wiss. in Wien, 93 (1886), 807-868.
J18.371

KAPTEYN W.,
[1] Expansion of functions in terms of Bernoulli polynomials, Proc. Intern. Math. Congress, Toronto, (1924), Reprinted v.1 (1967), 605-609.

KARAMATSU Y.,
[1] On Fermat's last theorem and the first factor of the class number of the cyclotomic field, 2, TRU Math., 16 (1980), no. 1, 23-29.
Z465.10010; M82a:10020; R1981,4A113

[2] Ribenboim's criteria and some criteria for the first case of Fermat's last theorem, TRU Math., 17 (1981), no.1, 25-38.
Z472.10021; M83a:10023; R1982,3A143

[3] A note on the first case of Fermat's last theorem. Prospects of mathematical science (Tokyo, 1986), pp. 73-77. World Sci. Publishing, Singapore, 1988.
Z654.o10017; M89i:11043

KARAMATSU Y.:see also ABE S., KARAMATSU Y.

KARANDE B.K., THAKARE N.K.,
[1] On the unification of Bernoulli and Euler polynomials, Indian J. Pure Appl. Math., 6 (1975), no. 1, 98-107.
Z343.33010; M54#110; R1977,6V412

KAREL M.L.,
[1] Fourier coefficients of certain Eisenstein series. Bull. Amer. Math. Soc., 78 (1972), 828-830.
Z255.10030; M45#6760; R1973,4A560

[2] Fourier coefficients of certain Eisenstein series. Ann. Math. (2), 99 (1974), no.1, 176-202.
Z279.10024; M49#8935; R1974,7A749

KASUBE H.: see GANDHI J.M., KASUBE H., SURYANARAYANA D.

KATAYAMA K.,
[1] On Ramanujan's formula for values of Riemann zeta function at positive odd integers, Acta Arith., 22 (1973), 149-155.
Z248.10032; M48#252; R1973,9A139

[2] On the values of Eisenstein series, Tokyo J. Math., 1 (1978), no. 1, 157-188.
Z391.10022; M80f:10029; R1979,1A148

[3] Corrections to: "On the values of Eisenstein series", Tokyo J. Math., 5 (1982), no. 1, 115-116.
M83j:10025

KATAYAMA K., OHTSUKI M.,
[1] On a theorem of Shintani, Tokyo J. Math., 16 (1993), no. 1, 155-170.
Z802.11015; M94e:11042

KATSURADA H.,
[1] An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree $3$, Nagoya Math. J. 146 (1997), 199-223.
Z882.11026; M98g:11051

[2] Power series and asymptotic series associated with the Lerch zeta-function, Proc. Japan Acad. Ser. A Math. Sci. 74 (1998), no. 10, 167-170.
M99m:11098

[3] Rapidly convergent series representations for $\zeta(2n+1)$ and their $\chi$-analogue, Acta Arith. 90 (1999), no. 1, 79-89.

KATSURADA M., MATSUMOTO K.,
[1] The mean values of Dirichlet $L$-functions at integer points and class numbers of cyclotomic fields. Nagoya Math. J., 134 (1994), 151-172.
Z806.11036; M95d:11108; R1995,6A292

[2] Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions. II. New trends in probability and statistics, Vol. 4 (Palanga, 1996), 119-134, VSP, Utrecht, 1997.
Z929.11027; M2000c:11145

KATZ N.M.,
[1] p-adic L-functions via moduli of elliptic curves, Proc. Symp. Pure Math., 29 (1975), 479-506.
Z317.14009; M55#5635

[2] The congruences of Clausen - von Staudt and Kummer for Bernoulli-Hurwitz numbers, Math. Ann., 216 (1975), 1-4.
Z303.10028; M52#8136; R1976,2A539

[3] Higher congruences between modular forms, Ann. of Math. (2), 101 (1975), no. 2, 332-367.
Z356.10020; M54#5120; R1976,1A516

[4] p-adic L-functions for CM-fields, Invent. Math., 49 (1978), no. 3, 199-297.
Z439.12010; M80h:10039; R1979,7A400

[5] Divisibilities, congruences and Cartier duality, J. Fac. Sci. Univ. Tokyo, Ser. IA, 28 (1981), no. 3, 667-678.
Z559.14032; M83h:10067; R1982,11A355

KAWASAKI T.,
[1] On the class number of real quadratic fields, Mem. Fac. Sci. Kyushu Univ., Ser. A, 35 (1981), no. 1, 159-171.
Z459.12003; M82g:12006; R1981,9A275

KAZANDZIDIS G.S.,
[1] On sums of like powers of the numbers less than $N$ and prime to $N$, Prakt. Akad. Athenon, 44 (1969), (1970), 148-158.
Z264.10009; M46#5230

[2] On the Bernoulli polynomials, Bull. Soc. Math. Grèce, 10 (1969), 151-182.
Z197,319; M43#4756

KELISKY R.P.,
[1] Congruences involving combinations of the Bernoulli and Fibonacci numbers, Proc. Nat. Acad. Sci. U.S.A., 43 (1957), no. 12, 1066-1069.
Z84,270; M19-941d; R1960,4A589

[2] On formulas involving both the Bernoulli and Fibonacci numbers, Scripta Math., 23 (1957), no. 1-4, 27-35.
Z84,66; M20#5300; R1960,3784

KELLER W., LÖH G.,
[1] The criteria of Kummer and Mirimanoff extended to include 22 consecutive irregular pairs, Tokyo J. Math., 6 (1983), no. 2, 397-402.
Z553.10009; M85h:11014; R1984,10A93

KERVAIRE M.A., MILNOR J.W.,
[1] Bernoulli numbers, homotopy groups, and a theorem of Rohlin, Proc. Intern. Congress of Math., Edinburgh 1958, Cambridge Univ. Press, 1960, 454-458.
Z119,385; M22#12531; R1961,8A349

[2] Groups of homotopy spheres, I, Ann. of Math., 77 (1963), no. 3, 504-537.
Z115,405; M26#5584; R1964,10A305

KHAN R.A.,
[1] A simple derivation of a formula for $\sum_{k=1}^n k^r$, Fibonacci Quart., 19 (1981), no. 2, 177-180.
M82e:05010; R1981,9V438

KHANNA I.K.,
[1] A new type of generalization of Bernoulli and Euler numbers and its applications, Progr. Math. (Varanasi), 20 (1986), no. 2, 83-89.
Z699.10022; M88g:11008

KHANNA I.K., PANDAY P.,
[1] Extended Bernoulli numbers and its applications, Ganita, 35 (1984), no. 1-2, 26-34 (1987).
Z632.10009

KHOVANSKII A.N.,
[1] Some identities connected with Bernoulli numbers. (Russian), Izvestiya Kazan. Filial. Akad. Nauka. SSSR. Ser. Fiz.-Mat. Tehn. Nauk., 1 (1948), 93-94.
M14-138c

KIDA M.,
[1] Kummer's criterion for totally real number fields. Tokyo J. Math., 14 (1991), no.2, 309-317.
Z758.11031; M92j:11135

KIM E.E., TOOLE B.A.,
[1] Ada and the first computer. Scientific American, May 1999, 76-81.

KIM HAN SOO, KIM TAEKYUN,
[1] On a $q$-analogue of the $p$-adic log gamma functions and related integrals. Number theory and related topics (Masan, 1994; Pusan, 1994), 67--75, Pyungsan Inst. Math. Sci., Seoul, 1995.
M97h:11013

[2] Remark on $q$-analogues of $p$-adic $L$-functions. Number theory and related topics (Masan, 1994; Pusan, 1994), 76--83, Pyungsan Inst. Math. Sci., Seoul, 1995.
M97g:11016

[3] On certain values of $p$-adic $q$-$L$-functions. Rep. Fac. Sci. Engrg. Saga Univ. Math. 23 (1995), no. 1-2, 1-7.
Z820.11071; M96f:11153; R1997,4A262

[4] Some congruences for Bernoulli numbers. II. Rep. Fac. Sci. Engrg. Saga Univ. Math. 24 (1996), no. 2, 5 pp.
Z869.11016; M98g:11018; R1996,12A142

[5] On $q$-$\log$-gamma-functions. Bull. Korean Math. Soc. 33 (1996), no. 1, 111-118.
Z865.11059; M97b:11025

[6] Remark on $p$-adic $q$-Bernoulli numbers. Algebraic number theory (Hapcheon/Saga, 1996). Adv. Stud. Contemp. Math. 1 (1999), 127-136.

KIM HAN SOO, LIM PIL-SANG, KIM TAEKYUN,
[1] A remark on $p$-adic $q$-Bernoulli measure. Bull. Korean Math. Soc. 33 (1996), no. 1, 39--44.
Z855.11062; M97b:11145

KIM JAE MOON,
[1] Class numbers of certain real abelian fields, Acta Arith., 72 (1995), no. 4, 335-345.
Z841.11056; M96j:11152; R1996,10A248

[2] Class numbers of real quadratic fields, Bull. Austral. Math. Soc., 57 (1998), no. 2, 261-274.
Z980.47404; M98m:11117

[3] Units and cyclotomic units in ${Z}\sb p$-extensions, Nagoya Math. J. 140 (1995), 101-116.
Z848.11055; M96m:11100

KIM TAEKYUN,
[1] An analogue of Bernoulli numbers and their congruences. Rep. Fac. Sci. Engrg. Saga Univ. Math., 22 (1994), no. 2, 21-26.
Z802.11007; M94m:11024

[2] On explicit formulas of $p$-adic $q$-$L$-functions. Kyushu J. Math., 48 (1994), no.1, 78-86.
Z817.11054; M95c:11140; R1996,8A219

KIM TAEKYUN: see also KIM HAN SOO, KIM TAEKYUN

KIMBALL B.F.,
[1] The application of Bernoulli polynomials of negative order to differencing, Amer. J. Math., 55 (1933), 399-416.
J59.I.367; Z7,211

[2] The application of Bernoulli polynomials of negative order to differencing. II, Amer. J. Math., 56 (1934), 147-152.
J60.II.1041; Z8,260

[3] A generalization of the Bernoulli polynomial of order one, Bull. Amer. Math. Soc., 41 (1935), 894-900.
J61.I.377; Z13,167

[4] The generalized Bernoulli polynomial and its relation to the Riemann zeta function (Abstract). Bull. Amer. Math. Soc., 39 (1933), 510-511.
J59.I.375

KIMURA N.,
[1] Kummersche Kongruenzen für die verallgemeinerten Bernoullischen Zahlen, J. Number Theory, 11 (1979), no. 2, 171-187.
Z406.10011; M81d:10008; R1980,1A112

[2] Über die Nullstellen der von Potenzsummen der natürlichen Zahlen definierten Polynome, Proc. Japan Acad. Ser. A, 58 (1982), no. 7, 326-328.
Z515.10012; M84k:10043; R1983,4A129

[3] On the degree of an irreducible factor of the Bernoulli polynomials, Acta Arith., 50 (1988), no. 3, 243-249.
Z655.10008; M89j:11019; R1989,3A251

KIMURA N., SIEBERT H.,
[1] Über die rationalen Nullstellen der von Potenzsummen der natürlichen Zahlen definierten Polynome. Proc. Japan. Acad. Ser. A, 56 (1980), no.7, 354-356.
Z462.10007; M82e:10013; R1981,3A96

KING, AUGUSTA ADA,
[1] Notes by the translator. (On L. F. Menabrea, "Sketch of the Analytical Engine Invented by Charles Babbage Esq."). In Richard Taylor (Ed.), Scientific Memoirs, Vol. III, Richard and John E. Taylor, London, 1843.

KINKELIN H.,
[1] Ueber eine mit der Gammafunction verwandte Transcendente und deren Anwendung auf die Integralrechnung. J. Reine Angew. Math., 57 (1860), 122-138.

KIRIYAMA H.: see ORIGUCHI T., KIRIYAMA H., MATSUOKA Y.

KIRSCHENHOFER P., PRODINGER H.,
[1] On some applications of formulae of Ramanujan in the analysis of algorithms. Mathematika, 38 (1991), no. 1, 14-33.
Z707.68024; M92h:68025

KIRSTEN K.,
[1] Inhomogeneous multidimensional Epstein zeta functions. J. Math. Phys., 32 (1991), no. 11, 3008-3014.
Z753.11032; M93a:11028

KISELEV A.A.,
[1] An expression for the number of classes of ideals of real quadratic fields by means of Bernoulli numbers. (Russian) Doklady Akad. Nauk. SSSR(N.S.), 61 (1948), 777-779.
Z35,022; M10-236h

[2] Vyrazhenie chisla klassov kvadratichnykh polej cherez chisla Bernulli [An expression for the number of classes of ideals of quadratic fields by means of Bernoulli numbers]. Nauchn. sessiya Leningradsk. Gos. Universiteta, Tezisy dokladov po sektsii Mat. Nauk, (1948), 37-39.

[3] O nekotorykh sravneniyakh chisla klassov idealov veshchestvennykh polej [On some congruences for the numbers of classes of ideals of real quadratic fields]. Uch. zap., Leningradsk. Gos. Universiteta, ser. mat. nauk, (1949), no. 16, 20-31.

[4] On the commumication "On the determination of the sum of quadratic residues of a prime $p= 4m+3$ by means of Bernoulli numbers" (Russian) In: Voronoi, G.F., Sobranie sochinenii v trekh tomakh. (Russian) [Collected works in three volumes.] Vol. III, Kiev, 1953, 203-204.
Z49,28; M16-2d; R1954,3228K

KISELEV A.A., SLAVUTSKII I.SH.,
[1] On the number of classes of ideals of a quadratic field and its rings. (Russian) Dokl. Akad. Nauk. SSSR, 126 (1959), 1191-1194.
Z92,274; M23#A141; R1960,4872

[2] Some congruences for the number of representations as sums of an odd number of squares. (Russian) Dokl. Akad. Nauk. SSSR, 143 (1962), 272-274.
Z121,264; M26#3687; R1962,10A73

[3] The transformation of Dirichlet's formulas and the arithmetical computation of the class number of quadratic fields. (Russian) 1964 Proc. Fourth All-Union Math. Congr. (Leningrad, 1961), Vol.II, pp. 105-112, Izdat. "Nauka", Leningrad.
Z201,378; M36#3748; R1964,11A108

[4] Rol' teorii chisel i mnogochlenov Bernulli v teorii chisel [The role of the theory of Bernoulli numbers and polynomials in number theory]. Tezisy dokl. konf. Leningradsk. otdeleniya Sovetsk. nats. ob'edineniya istorikov estestvoznaniya i tekhniki, Leningrad, (1966), 9.

[5] Chislo klassov idealov kvadratichnogo polya i chisla Bernulli [The number of classes of ideals of a quadratic field and Bernoulli numbers]. Tezisy sektsyii No. 3 Mezhdunarodn. kongressa matematikov, Moskva, (1966), 15-16.

KISHORE N.,
[1] The Rayleigh function, Proc. Amer. Math. Soc., 14 (1963), 527-533.
Z117,299; M27#1633; R1964,5B48

[2] A representation of the Bernoulli number $B_n$, Pacific J. Math., 14 (1964), 1297-1304.
Z132,299; M30#1082; R1966,2B61

[3] Congruence properties of the Rayleigh functions and polynomials, Duke Math. J., 35 (1968), 557-562.
Z182,66; M37#3995; R1969,6B90

KLEBOTH H.,
[1] Untersuchung über Klassenzahl und Reziprozitätsgesetz im Körper der 6l-ten Einheitswurzeln und die Diophantische Gleichung $x^{2l}+3ly^{2l}=z^{2l}$ für eine Primzahl $l$ grösser als 3, Dissertation, Univ. Zürich, 1955, 37 pp.
M20#4537; R1962,11A123D

KLINE M.,
[1] Euler and infinite series, Math. Mag., 56 (1983), no. 5, 301-315.
Z526.01015; M86a:01020; R1984,7A11

KLINOWSKI J.: see CVIJOVIC D., KLINOWSKI J.

KLUYVER J.C.,
[1] Der Staudt-Clausen'sche Satz., Math. Ann., 53 (1900), 591-592.
J31.198

[2] Ontwikkelingscoëfficiënten, die eenige overeenkomst met de getallen van Bernoulli vertoonen, Nieuw Arch. Wisk. (2), 5 (1901), 249-254.
J32.282

[3] An analytical expression for the greatest common divisor of two integers, Proc. Royal Acad. Amsterdam, 5 (1903), 658-662.

[4] Über die Summen der gleich hohen inversen Potenzen der ganzen Zahlen, Handl. Neder. Nat. en Geneesk. Congr., 10 (1905), 181-184 . (original title: Over de sommen van gelijknamige machten der omgekeerden van de geheele getallen).
J36.341

[5] Verallgemeinerung einer bekannten Formel, Nieuw Arch. Wisk. (2), 4 (1899/1900), 284-291.
J31.437

KNAR J.,
[1] Entwicklung der vorzüglichsten Eigenschaften einiger mit den goniometrischen zunächst verwandten Functionen, Arch. Math. und Phys., 27 (1856), 365-470.

KNOPP K.,
[1] Theorie und Anwendung der unendlichen Reihen, 4-te Auflage, Springer-Verlag, Berlin-Heidelberg, 1947, xii + 583 pp.
Z31,118; M10-446a

KNUTH D.E.,
[1] Johann Faulhaber and sums of powers. Math. Comp., 61 (1993), no. 203, 277-294.
Z797.11026; M94a:11030

KNUTH D.E., BUCKHOLTZ T.J.,
[1] Computation of tangent, Euler and Bernoulli numbers, Math. Comp., 21 (1967), 663-688.
Z178,44; M36#4787; R1968,6B856

KNUTH D.E.: see also GRAHAM R.L., KNUTH D.E., PATASHNIK O.

KOBELEV V.V.,
[1] A proof of Fermat's theorem for all prime exponents less than 5500. (Russian) Dokl. Akad. Nauk. SSSR, 190 (1970), 767-768.
Z205,65; M41#3363; R1970,7A149

KOBLITZ N.,
[1] p-adic numbers, p-adic analysis and zeta-functions, Springer-Verlag, New York, 1977. (Russk. perevod 83i:12013).
Z364.12015*; M57#5964; R1978,8A366K

[2] Interpretation of the p-adic log gamma functions and Euler constant using the Bernoulli measure, Trans. Amer. Math. Soc., 242 (1978), 261-269.
Z(358.12010)379.12011; M58#10836; R1979,2A255

[3] A new proof of certain formulas for p-adic L-functions, Duke Math. J., 46 (1979), 455-468.
Z409.12028; M80f:12011; R1980,2A355

[4] p-adic analysis: a short course on recent works, London Math Soc. Lecture Note Series, No. 46, 1980.
Z439.12011*; M82c:12014; R1981,5A374

[5] On Carlitz's q-Bernoulli numbers, J. Number Theory, 14 (1982), no. 3, 332-339.
Z501.12020; M83k:12017; R1982,12A354

[6] q-extension of the p-adic gamma function, II, Trans. Amer. Math. Soc., 273 (1982), no. 1, 111-129.
Z508.12016; M84a:12024; R1983,4A364

[7] Introduction to elliptic curves and modular forms, Graduate Texts in Mathematics No. 97. Springer-Verlag, New York- Berlin, 1984. viii + 248pp.
Z553.10019*; M86c:11040; R1985,5A394K

[8] p-adic congruences and modular forms of half integer weight, Math. Ann., 274 (1986), no. 2, 199-220.
Z571.10030, 582.10019; M88a:11043; R1986,11A576

[9] Congruences for periods of modular forms, Duke Math. J., 54 (1987), no. 2, 361-373.
Z628,10032; M88k:11030; R1988,5A434

[10] Jacobi sums, irreducible zeta-polynomials and cryptography. Canad. Math. Bull., 34 (1991), no. 2, 229-235.
Z(725.11028) 686.12011; M92e:11067

KOCH H.,
[1] Algebraic number theory. (Russian) Itogi Nauki i Tekhniki, Number Theory, 2 (1990), 5-308.
Z722.11001; M92a:11118b

[2] Introduction to classical mathematics. I. From the quadratic reciprocity law to the uniformization theorem. Mathematics and its Applications, 70. Kluwer Akademic Publ., Dordrecht, 1991. xviii+453pp.
Z733.00001; M92k:00010

KOECHER M.: see EBBINGHAUS H.-D. et al.

KOEPF W.,
[1] On two conjectures of M.S. Robertson. Complex Variables, Theory and Appl., 16 (1991), no. 2/3, 127-130.
Z745.30004; M92f:30004

KÖHLER G.,
[1] Observations on Hecke eigenforms on the Hecke groups $G(\sqrt{2})$ and $G(\sqrt{3})$, Abh. Math. Sem. Univ. Hamburg, 55 (1985), 75-89.
Z565.10022, 575.10018; M87e:11067; R1986,8A536

KOHNEN W.,
[1] On the proportion of quadratic character twists of $L$-functions attached to cusp forms not vanishing at the central point, J. Reine Angew. Math. 508 (1999), 179-187.

KOHNEN W., ZAGIER D.,
[1] Modular forms with rational periods. Modular forms (Durham, 1983), 197-249, Horwood, Chichester, 1984.
Z618.10019; M87h:11043; R1987,5A440

KOLK J.A.C.: see BEUKERS F., KOLK J.A.C., CALABI E.

KOLSCHER M.,
[1] Die Potenzsummen der natürlichen Zahlen, Math. Naturwiss. Unterricht, 6 (1954), 307-310.
M15-684f

KOLSTER M.,
[1] On the Birch-Tate conjecture for maximal real subfields of cyclotomic fields, Lecture Notes Math., 1046 (1984), 229-234.
Z528.12009; M86b:11079; R1984,9A305

[2] Remarks on étale $K$-theory and Leopoldt's conjecture. Séminaire de théorie des nombres, Paris, 1991-92, 37-62, Progr. Math., 116, Birkhäuser, Boston, MA, 1993.
M95i:19006

KOLYVAGIN V.A.,
[1] Euler systems. In: The Grothendieck Festschrift Vol. II, Progr. Math., 87, Birkhäuser Boston, Boston, MA, 1990, 435-483.
Z742.14017; M92g:11109

[2] Fermat equations over cyclotomic fields, Proc. Steklov Inst. Math., 208 (1995), 146-165; translation from Tr. Mat. Inst. Steklova, 208 (1995), 163-185.
Z881.11037; R1996,4A272

KORTEWEG D.J.,
[1] Over benaderings-formelen voor de som von reeksen welke uit een groot aantal termen bestaan, Nieuw Arch. Wiskunde, 2 (1876), 161-176.
J8.134

KOSEKI H.: see HASHIMOTO K., KOSEKI H.

KOSHLYAKOV N.S.,
[1] Ob odnom obobshchenii polinomov Bernulli [An extension of Bernoulli's polynomials]. Mat. Sbornik 42 (1935), 425-434.
J61.I.378; Z13,167

[2] Remarks on the paper of I.J. Schwatt "The sum of like powers of a series of numbers forming an arithmetical progression and the Bernoulli numbers." (Russian), Mat. Sb., 40 (1933), 528.
J59.II.895; Z9.074

KOTIAH T.C.T.,
[1] Sums of powers of integers - a review. Internat. J. Math. Ed. Sci. Tech., 24 (1993), no. 6, 863-874.
Z806.11015; M94g:11016

KOUNCHEV O.: see DRYANOV D., KOUNCHEV O.

KOUTSKY K.,
[1] K Lerchovym pracim o Fermatove kvotientu [On Lerch's work on the Fermat quotient], Prace Moravske Prirodovedecke Spolecnosti, 18 (1947), 1-7.

KOZUKA K.,
[1] On abelian extensions over cyclotomic $Z_{p_1}\times \cdots \times Z_{p_t}$-extension, Mem. Fac. Sci., Kyushu Univ., Ser A, 38 (1984), no. 2, 141-149.
Z528.12009; M85i:11095; R1985,6A294

[2] on a p-adic interpolating power series of the generalized Euler numbers, J. Math. Soc. Japan, 42 (1990), no. 1, 113-125.
Z706.11068; M90j:11020; R1990,8A87

[3] On the values of the p-adic valuation of the generalized Euler numbers, Mem. Fac. Sci. Kyushu Univ. Ser. A, 43 (1989), no. 2, 37-53.
Z705.11007; M91a:11062a; R1990,7A292

[4] On the $\ mu$-invariant of an interpolating power series of the generalized Euler numbers, Mem. Fac. Sci. Kyushu Univ. Ser. A, 43 (1989), no. 2, 43-53.
Z706.11069; M91a:11062b; R1990,7A293

[5] On the $\mu$-invariants of certain $p$-adic $L$-functions attached to the formal multiplicative group. Res. Rep. Miyakonojo Nat. Coll. Technol., 1994, no. 28, 1-10.
R1994,8A372

KRAFT J. S.,
[1] Class numbers and Iwasawa invariants of quadratic fields. Proc. Amer. Math. Soc. 124 (1996), no. 1, 31-34.
Z846.11059; M96d:11112; R1996,7A228

KRALL H.L.,
[1] Self-adjoint differential expressions, Amer. Math. Monthly, 67 (1960), no. 9, 876-878.
Z145.32501; M24#A270; R1961,12B123

KRAMER D.,
[1] Spherical polynomials and periods of a certain modular form, Trans. Amer. Math. Soc., 294 (1986), no. 2, 595-605.
Z592.10017; M87e:11061; R1986,12A587

[2] On the values at integers of the Dedekind zeta function of a real quadratic field, Trans. Amer. Math. Soc., 299 (1987), no. 1, 59-79.
Z606.12007; M88a:11123; R1987,7A113

KRASNER M.,
[1] Sur le premier cas du théorème de Fermat, C.R. Acad. Sci., Paris 199 (1934), 256-258.
J60.I.129; Z10,007

KRAUSE M.,
[1] Zur Theorie der ultra-Bernoullischen Zahlen und Funktionen, Berichte Verh. Kgl. Gesells. Wiss., Leipzig, 54 (1902), 139-205.
J33.971

[2] Über Bernoulische Zahlen und Funktionen im Gebiete der Funktionen zweier veränderlicher Grössen, Berichte Verh. Kgl. Gesells. Wiss., Leipzig, 55 (1903), 39-62.
J34.485

[3] Zur Theorie der Eulerschen und Bernoullischen Zahlen, Monatsh. Math. Phys., 14 (1903), 305-324.
J34.483

[4] Über die Bernoullische Funktion zweier veränderlicher Grössen, Arch. Math. und Phys. (3), 4 (1903), 293-295.
J34.485

KREWERAS G.,
[1] An additive generation for the Genocchi numbers and two of its enumerative meanings. Bull. Inst. Combin. Appl. 20 (1997), 99-103.
Z879.05001; M98d:05010

[2] Sur les permutations comptées par les nombres de Genocchi de 1-ière et 2-ième espèce. (French) [Permutations enumerated by Genocchi numbers of the first and the second kind] European J. Combin. 18 (1997), no. 1, 49-58.
Z869.05002; M97k:05010

KRICK M.S.,
[1] On the coefficients of $cosh x/cos x$, Math. Mag., 34 (1960), no. 1, 37-40.
Z105,264; R1961,6B334

KRIEG A.: see EIE M., KRIEG A.

KRISHNAMACHARY C., BHIMASENA RAO M.,
[1] On a table for calculating Eulerian numbers based on a new method. Proc. London Math. Soc. (2), 22 (1923), 73-80.
J49.167

KRONECKER L.,
[1] Sur quelques fonctions symmetriques et sur les nombres de Bernoulli, J. Math. Pure Appl. (2), 1 (1856), 385-391.

[2] Démonstration d'un Théorème de Kummer, J. Math. Pure Appl., (2), 1 (1856), 396-398.

[3] Über die Bernoullischen Zahlen (Bermerkungen zu der Abhandl. des Herrn Worpitzky), J. Reine Angew. Math., 94 (1883), 268-270.
J15.201

[4] Über eine bei Anwendung partieller Integration nützliche Formel, Sitz. Kgl. Preuss. Akad. Wiss., Berlin, (1885), 841-862.
J17.251

KROUKOVSKI B.V.,
[1] Sur les nombres semblables aux nombres Bernouilliens et Eulériens. Les nombres pseudo-cotangentiels (Ukrainian; French summary). J. Inst. Math. Kiev., (1934-35), no. 1, 43-62.
J61.II.985; Z12.151

KUBERT D.S.,
[1] The universal ordinary distribution, Bull. Soc. Math. France, 107 (1979), no. 2, 179-202.
Z409.12021; M81b:12004; R1980,2A357

[2] The 2-divisibility of the class number of cyclotomic fields and the Stickelberger ideal, J. Reine Angew. Math., 369 (1986), 192-218.
Z584.12003; M88a:11108

KUBERT D., LANG S.,
[1] Cartan-Bernoulli numbers as values of L-series, Math. Ann., 240 (1979), no. 1, 21-26.
Z(377.12010),393.12020; M81b:10027; R1979,7A404

[2] Modular units inside cyclotomic units, Bull. Soc. Math. France, 107 (1979), fasc. 2, 161-178.
Z409.12007; M81k:12006; R1980,2A356

[3] Modular units, Springer-Verlag, New York-Berlin, 1981, xiii + 358pp. (Grundl. Math. Wiss., No. 244.)
Z492.12002*; M84h:12009; R1982,3A406,7A382

KUBOTA T., LEOPOLDT H.W.,
[1] Eine p-adische Theorie der Zetawerte, Teil 1: Einführung der p-adischen Dirichletschen L-Funktionen, J. Reine Angew. Math., 214/215 (1964), 328-339.
Z186,91; M29#1199; R1965,4A90

KUDO A.,
[1] On a class number relation of imaginary abelian fields, J. Math. Soc. Japan, 27 (1975), 150-159.
Z294.12004; M50#12968; R1975,9A292

[2] On generalization of a theorem of Kummer, Mém Fac. Sci. Kyushu Univ., Ser. A, 29 (1975), no. 2, 255-261.
Z314.12011; M53#8010; R1976,3A369

[3] Generalized Bernoulli numbers and the basic $ Z_p$-extensions of imaginary quadratic fields, Mém. Fac. Sci. Kyushu Univ., Ser. A, 32 (1978), no. 2, 191-198.
Z425.12007; M80e:12012; R1979,2A260

[4] On $p$-adic Dedekind sums, II. Mem. Fac. Sci. Kyushu Univ., Ser. A, 45 (1991), no.2, 245-284.
Z751.11031; M93g:11120; R1992,7A355

[5] Reciprocity formulas for $p$-adic Dedekind sums, Bull. Fac. Liberal Arts Nagasaki Univ., 34 (1994), no. 2, 97-101.
Z813.11065; M95c:11142

[6] On $p$-adic Dedekind sums, Nagoya Math. J. 144 (1996), 155-170.
Z872.11051; M97m:11143; R1997,11A270

KUDRYAVTSEV V.A.,
[1] Summirovanie stepenej natural'nogo ryada i chisla Bernulli [Summation of powers of natural series and Bernoulli numbers]. Moskva, 1936.

KUHN P.,
[1] Zu den Mittelwerten zahlentheoretischer Funktionen. Norske Vid. Selsk. Forhdl., Trondheim, 14 (1941), no. 42, 157-160.
J67.131; M8-503d

KUMMER E.E.,
[1] Beweis des Fermat'schen Satzes der Unmöglichkeit von $x^{\lambda}+y^{\lambda}=z^{\lambda}$ für eine unendliche Anzahl Primzahlen $\lambda$, Monatsb. Akad. Wiss. Berlin, (1847), 132-141, 305-319.

[2] Zwei besondere Untersuchungen über die Classen-Anzahl und über die Einheiten der aus $\lambda$-ten Wurzeln der Einheit gebildeten complexen Zahlen, J. Reine Angew. Math., 40 (1850), no. 2, 117-129. / Coll. Papers, v.1., Berlin e.a.: Springer-Verlag, 1975. viii + 957pp.
Z327.01019*; M57#5650a; R1976,1A127K

[3] Allgemeiner Beweis des Fermat'schen Satzes, dass die Gleichung $x^{\lambda}+y^{\lambda}=z^{\lambda}$ durch ganze Zahlen unlösbar ist, für alle diejenigen Potenz-Exponenten $\lambda$, welche ungerade Primzahlen sind und in den Zählern der ersten $({\lambda}-3)/2$ Bernoulli'schen Zahlen als Factoren nicht vorkommen, J. Reine Angew. Math., 40 (1850), 131-138.

[4] Mémoire sur la théorie des nombres complexes composés de racines de l'unité et de nombres entiers, J. Math. Pure Appl., 16 (1851), 377-498.

[5] Über eine allgemeine Eigenschaft der rationalen Entwicklungscoefficienten einer bestimmten Gattung analytischer Functionen, J. Reine Angew. Math., 41 (1851), 368-372.

[6] Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math., 44 (1852), no. 2, 93-146.

[7] Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math., 56 (1859), 270-279.

[8] Einige Sätze über die aus den Wurzeln der Gleichung $\alpha^{\lambda} = 1$ gebildeten complexen Zahlen, für den Fall, dass die Klassenzahl durch $\lambda$ theilbar ist, nebst Anwendung derselben auf einen weiteren Beweis des letzten Fermats'chen Lehrsatzes, Abhandl. Akad. Wiss. Berlin, Math., (1857), (1858), 41-74. (See also Auszug, Monatsb. Akad. Wiss. Berlin, (1857), 275-282.)

[9] Über diejenigen Primzahlen $\lambda$, für welche die Klassenzahl der aus $\lambda$-ten Einheitswurzeln gebildeten complexen Zahlen durch $\lambda$ theilbar ist, Monatsb. Akad. Wiss. Berlin, (1874), 239-248.
J6.117

[10] Die Briefe an Leopoldt Kronecker, Abhandl. zur Geschichte der Math. Wiss., Leipzig, (1910), Heft 29.
J41.15

KUNDERT E.G.,
[1] Basis in a certain completion of the s-d-ring over the rational numbers. I, II. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 64 (1978), no. 5, 423-428; no. 6, 543-547.
Z428:13013; M81j:13026a,b; R1980,7A204; 7A205

[2] The Bernoullian of a matrix (A generalization of Bernoulli numbers), Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 72 (1982), (1983), no. 6, 315-317.
Z523.10005; M85g:05021; R1984,6A87

[3] A von Staudt-Clausen theorem for certain Bernoullian-like numbers and regular primes of the first and second kind. Fibonacci Quart., 28 (1990), no. 1, 16-21.
Z694.10013; M91e:11022; R1991,2A107

KUO HUAN-TING,
[1] A recurrence formula for $\zeta(2n)$, Bull. Amer. Math. Soc., 55 (1949). 573--574.
Z032.34501; M10,683d

KURIHARA A.,
[1] On the values at non-positive integers of Siegel's zeta functions of $ Q$-anisotropic quadratic forms with signature $(1, n-1)$. J. Fac. Sci. Univ. of Tokyo Sect. IA Math., 28 (1981), no.3, 567-584.
Z495.10019; M84a:10021

KURIHARA F.,
[1] On the p-adic expansion of units of cyclotomic fields, J. Number Theory, 32 (1989), no. 2, 226-253.
Z689.12005; M90k:11138; R1990,2A337

KURIHARA M.,
[1] Some remarks on conjectures about cyclotomic fields and $K$-groups of $ Z$. Compositio Math., 81 (1992), no. 2, 223-236.
Z747.11055; M93a:11091

KURT V.,
[1] Remarks on higher-dimensional Dedekind sums, Math. Japon. 45 (1997), no. 2, 297-301.
Z882.11024; M98c:11037

KÜTTNER W.,
[1] Zur Theorie der Bernoullischen Zahlen, Zeits. für Math. u. Phys., 24 (1879), 250-252.
J11.188

KUZMIN L.V.,
[1] Algebraic number fields. (Russian) Algebra. Topology. Geometry, Vol. 22, (Itogi. Nauki i Tekhniki, Akad. Nauk. SSSR), Moscow, 1984, 117-204.
Z563.12002; M86f:11076; R1985,1A446

KUZNETSOV A. G., PAK I. M., POSTNIKOV A. E.,
[1] Increasing trees and alternating permutations. (Russian) Uspekhi Mat. Nauk 49 (1994), no. 6(300), 79-110. Translated in: Russian Math. Surveys 49 (1994), no. 6, 79-114.
Z842.05025; M96e:05048

KUZUMAKI T.: see KANEMITSU S., KUZUMAKI T.

KWON SOUN-HI: see CHANG KU-YOUNG, KWON SOUN-HI


LACROIX S.F.,
[1] Traité des différences, Paris, 1819, t.2.

LAFORGIA A.,
[1] Inequalities for Bernoulli and Euler numbers, Boll. Un. Mat. Ital. A(5), 17 (1980), no. 1, 98-101.
Z498.10011; M81g:10028; R1980,11V466

LAGRANGE R.,
[1] Mémoire sure les suites de polynomes. Acta Math., 51 (1928), 201-309.
J54.484

LAI K.F.: see EIE M., LAI K.F.

LAMPE E.,
[1] Auszug eines Schreibens an Herrn Stern über die Verallgemeinerung einer Jacobi'schen Formel, J. Reine Angew. Math., 84 (1878), 270-272.
J9.176

LAMPE E.: see also BARNIVILLE J.J., DICKSON J.D.H., LAMPE E.

LAN YIZHONG,
[1] A limit formula for $\zeta(2k+1)$. J. Number Theory, 78 (1999), no. 2, 271-286.

LANG H.,
[1] Über eine Gattung elementar-arithmetischer Klasseninvarianten reell-quadratischer Zahlkörper, J. Reine Angew. Math., 233 (1968), 123-175.
Z165,365; M39#168; R1969,10A72

[2] Über Anwendungen höherer Dedekindscher Summen auf die Struktur elementar-arithmetischer Klasseninvarianten reell-quadratischer Zahlkörper, J. Reine Angew. Math., 254 (1972), 17-32.
Z244.12012; M45#8637; R1972,12A141

[3] Über Bernoullische Zahlen in reell-quadratischen Zahlkörpern, Acta Arith., 22 (1973), 423-437.
Z231.12004; M47#6651; R1973,11A120

[4] Über verallgemeinerte Bernoullische Zahlen und die Klassenzahl reell-quadratischer Zahlkörper, Acta Arith., 23 (1973), 13-18.
Z231.12005; M48#3914; R1974,1A175

[5] Über die Klassenzahlen eines imaginären bizyklischen Zahlkörpers und seines reell-quadratischen Teilkörpers, 2, J. Reine Angew. Math., 267 (1974), 175-178.
Z285.12013; M49#7238; R1974,12A133

[6] Über verallgemeinerte Dedekindsche Summen, Strahlklasseninvarianten reell-quadratischer Zahlkörper und die Klassenzahl des q-ten Kreisteilungskörpers, J. Reine Angew. Math., 338 (1983), 95-106.
Z506.12010; M84m:12006; R1983,7A151

[7] Über die Werte $\zeta (2-p,K)$ der Zetafunktion einer Idealklasse aus einem reell-quadratischen Zahlkörper, J. Reine Angew. Math., 361 (1985), 35-46.
Z559.12008; M87g:11153; R1986,4A397

[8] Über die Restklasse modulo $2^{e+2}$ des Wertes $2^en{\zeta}(1-2^en, K)$ der Zetafunktion einer Idealklasse aus dem reell-quadratischen Zahlkörper $ Q(\sqrt(D))$ mit $D \equiv 3 (mod 4)$, Acta Arith., 51 (1988), 277-292.
Z621.12014; M89i:11125; R1989,6A128

[9] Kummersche Kongruenzen für die normierten Entwicklungskoeffizienten der Weierstrassschen $\wp$-Funktion. Abh. Math. Sem. Univ. Hamburg, 33 (1969), no. 3-4, 183-196.
Z183,313; M41#6780; R1970,3B71

[10] Über die Werte der Zetafunktionen einer Idealklasse und die Kongruenzen von N. C. Ankeny, E. Artin und S. Chowla für die Klassenzahl reell-quadratischer Zahlkörper. J. Number Theory, 48 (1994), no. 1, 102-108.
Z810.11062; M95i:11133

LANG S.,
[1] Elliptic Functions, Addison-Wesley, London, 1974. xiii + 326 pp.
Z316.14001*; M53#13117; R1975,9A353

[2] Introduction to Modular Forms, Springer-Verlag, Berlin, 1976, Ch. 6, 10, 13.
Z344.10011*; M55#2751; R1977,7A118K

[3] Cyclotomic fields. Graduate Texts in Mathematics, Vol. 59. Springer-Verlag, New York, 1978.
Z395.12005*; M58#5578; R1979,11A312K

[4] Cyclotomic fields. II. Graduate Texts in Mathematics, 69. Springer-Verlag, New York, 1980.
Z435.12001*; M81i:12004; R1981,9A274K

[5] Units and class groups in number theory and algebraic geometry, Bull. Amer. Math. Soc., 6 (1982), no. 3, 253-316.
Z482.12002; M83m:12002; R1983,1A344

[6] Introduction to Arakelov theory. Springer-Verlag, New York-Berlin, 1988. x+187 pp.
Z667.14001; M89m:11059

[7] Old and new conjectured Diophantine inequalities, Bull. Amer. Math. Soc. (N.S.), 23 (1990), no. 1, 37-75.
Z714.11034; M90k:11032

[8] Cyclotomic Fields I and II. Combined second edition. With an appendix by Karl Rubin. Graduate Texts in Mathematics, 121. Springer Verlag, Berlin etc., 1990, xviii+433p.
Z704.11038; M91c:11001

LANG S.: see also KUBERT D., LANG S.

LANGMANN K.,
[1] Eine enliche Formel für die Anzahl der Teiler von $n$. J. Number Theory, 11 (1979), no. 1, 116-127.
Z397.10038; M80g:10044; R1979,9A90

LAPLACE P.-S.,
[1] Mémoire sur l'usage du calcul aux différences partielles dans la théorie des suites, Mém. de math. et phys. Acad. Sci. (Paris), (1777), 99-122.

LASSÁK M.: see JAKUBEC S., LASSÁK M.

LE MAOHUA,
[1] A note on the generalized Bernoulli sequences, Ars Combin., 44 (1996), 283-286.
Z888.11010; M97g:05005

LE BESGUE V.A.,
[1] Note sur les nombres de Bernoulli, C.R. Acad. Sci., Paris, 58 (1864), 853-856, 937-938.

LE BIHAN P.,
[1] L'équation diophantienne $m^q = \sum_{x=0}^{n-1}(kx+1)^p$, preprint, Mathématiques, Faculté des Sciences, Brest (France).

[2] Sur un résultat de J.J. Schäffer concernant l'équation $\sum_{k=1}^nk^p = m^q$ , preprint, Mathématiques, Faculté des Sciences, Brest (France).

[3] L'équation $m^q = \sum_{x=0}^{n-1}(kx+1)^p$ , preprint, Mathématiques, Faculté des Sciences, Brest (France).

LECLERC M.: see BUTZER M. et al

LEE JUNGSEOB,
[1] Integrals of Bernoulli polynomials and series of zeta function, Commun. Korean Math. Soc. 14 (1999), no. 4, 707-716.

LEEMING D.J.,
[1] Some properties of a certain set of interpolating polynomials, Canad. Math. Bull. 18 (1975), no. 4, 529-537.
Z317.41003; M53#1098; R1977,10V374

[2] An asymptotic estimate for the Bernoulli and Euler numbers, Canad. Math. Bull., 20 (1977), no. 1, 109-111.
Z358.10006; M56#5412; R1978,1V470

[3] The real zeros of the Bernoulli polynomials, J. Approx. Theory, 58 (1989), no. 2, 124-150.
Z692.41006; M90k:33029; R1990,4B130

[4] The coefficients of sinh $xt/\sin t$ and the Bernoulli polynomials. Internat. J. Math. Ed. Sci. Tech. 28 (1997), no. 4, 575-579.
Z970.56671; M98m:33023

LEEMING D.J., MACLEOD R.A.,
[1] Some properties of generalized Euler numbers, Canad. J. Math., 33 (1981), no. 3, 606-617.
Z419.10017; M82j:10025; R1982,4V517

[2] Generalized Euler number sequences: asymptotic estimates and congruences, Canad. J. Math., 35 (1983), no. 3, 526-546.
Z493.10015, 516.10007; M85c:11021; R1984,11A36

LEGENDRE A.M.,
[1] Traité des fonctions elliptiques, 1, Paris, 1825.

LEHMER D.H.,
[1] Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Ann. of Math., 36 (1935), no. 3, 637-649.
J61.I.66; Z12,151

[2] An extension of the table of Bernoulli numbers, Duke Math. J., 2 (1936), 460-464.
J62.I.50; Z15,003

[3] On the maxima and minima of Bernoulli polynomials, Amer. Math. Monthly, 47 (1940), 533-538.
J66.319; M2-43a

[4] The lattice points of an $n$-dimensional tetrahedron, Duke Math. J. 7 (1940), 341-353.
Z024.14901; M2,149g

[5] Generalized Eulerian numbers, J. Combinat. Theory, Ser. A, 32 (1982), no. 2, 195-215.
Z484.05006; M83k:10026; R1982,11V558

[6] Some properties of the cyclotomic polynomial, J. Math. Anal. Appl., 15 (1966), 105-117.
Z168,293; M33#5606; R1967,4A144

[7] A new approach to Bernoulli polynomials, Amer. Math. Monthly, 95 (1988), no. 10, 905-911.
Z663.10009; M90c:11014

[8] The sum of like powers of the zeros of the Riemann zeta function, Math. Comp., 50 (1988), no. 181, 265-273.
Z664.10029; M88m:11073; R1988,9A122

LEHMER D.H., LEHMER E., VANDIVER H.S.,
[1] An application of high-speed computing to Fermat's last theorem, Proc. Nat. Acad. Sci. USA, 40 (1954), 25-33.
Z55,40; M15-778f; R1955,1638

LEHMER E.,
[1] A note on Wilson's quotient, Amer. Math. Monthly, 44 (1937), 237-238.
J56.106

[2] On congruences involving Bernoulli numbers and quotients of Fermat and Wilson, Ann. Math. (2), 39 (1938), 350-360.
J64.II.95; Z19,005

LEHMER E.: see also LEHMER D.H., LEHMER E., VANDIVER H.S.

LE LIDEC P.,
[1] Sur une forme nouvelle des congruences de Kummer-Mirimanoff, C.R. Acad. Sci. Paris, 265 (1967), no. 3, A89-A90.
Z154,296; M36#108; R1968,5A195

[2] Nouvelle forme des congruences de Kummer-Mirimanoff pour le premier cas du théorème de Fermat, Bull. Soc. Math. France, 97 (1969), 321-328.
Z188,101; M41#6768; R1970,8A114

LÉMERAY E.M.,
[1] Sur certains nombres analogues aux nombres de Bernoulli, Nouv. Ann. Math. (4), 1 (1901), 509-516.
J32.283

LENSE J.,
[1] Über die Nullstellen der Bernoullischen Polynome, Monatsh. Math., 41 (1934), 188-190.
J60.296; Z9,311

LEOPOLDT H.W.,
[1] Eine Verallgemeinerung der Bernoullischen Zahlen, Abh. Math. Sem. Univ. Hamburg, 22 (1958), 131-140.
Z80,30; M19-1161e; R1958,9758

[2] Über Klassenzahlprimteiler reeller abelscher Zahlkörper als Primteiler verallgemeinerter Bernoullischer Zahlen, Abh. Math. Sem. Univ. Hamburg, 23 (1959), 36-47.
Z86,31; M21#1967; R1960,3770

[3] Über Fermatquotienten von Kreiseinheiten und Klassenzahlformeln modulo p, Rend. Circ. Mat., Palermo (2), 9 (1960), 39-50.
Z98,35; M24#A722; R1961,10A142

[4] Zur Arithmetik in abelschen Zahlkörpern, J. Reine Angew. Math., 209 (1962), 54-71.
Z204,71; M25#3034; R1963,5A246

[5] Zum wissenschaftlichen Werk von Helmut Hasse, J. Reine Angew. Math., 262/263 (1973), 1-17.
Z268.01011; M58#87; R1974,7A33

[6] Eine p-adische Theorie der Zetawerte, 2: Die p-adische $\Gamma$-Transformation, J. Reine Angew. Math., 274/275 (1975), 224-239.
Z309.12009; M52#351; R1976,1A380

LEOPOLDT H.W.: see also KUBOTA T., LEOPOLDT H.W.

LE PAIGE C.: see le PAIGE C.

LEPKA K.,
[1] Historie Fermatovych kvocientu (Fermat - Lerch), Dissertation, Brno, 1998.

LERCH M.,
[1] Zur Theorie des Fermatschen Quotienten ${{a^p-1\over{p}}=q(a)$, Math. Ann., 60 (1905), 471-490.
J36.266

LETTL G.,
[1] Stickelberger elements and cotangent numbers. Exposition. Math., 10 (1992), no. 2, 171-182.
Z757.11038; M93g:11111; R1993,7A287

LEVINE J.: see CARLITZ L., LEVINE J.

LI JIAN YU: see CHEN JING RUN, LI JIAN YU

LICHTENBAUM St.,
[1] On p-adic L-fucntions associated to elliptic curves, Invent. Math., 56 (1980), no. 1, 19-55.
Z425.12017; M81j:12013; R1980,5A422

le LIDEC P.: see LE LIDEC P.

LIÉNARD R.,
[1] Tables fondamentales à 50 décimales des sommes $S_n$, $U_n$, ${\Sigma_n$. Centre de Documentation Universitaire, Paris, 1948. 54 pp.
M10-149i

LIGOWSKI W.,
[1] Die Bestimmung der Summe $\Sigma x^r$, Arch. Math. und Phys., 65 (1880), 329-334.
J12.191

LIKHIN V.V.,
[1] Razvitie teorii chisel i funktsij Bernulli v trudakh russkikh i sovetskikh matematikov [Development of the theory of Bernoulli numbers and functions in the works of Russian and Soviet mathematicians]. Dissertatsiya, Moskovsk. Gos. Universitet [Dissertation, Moscow State University], 1954.

[2] Osnovnye etapy razvitiya teorii chisel i funktsij Bernulli [The main stages of development of the theory of numbers and functions of Bernoulli]. Trudy instituta istorii estestvoznaniya i tekhniki Akad. Nauk SSSR 19 (1957), 411-430.
R1961,4A29

[3] Teoriya chisel i funktsij Bernulli i ee razvitie v trudakh otechestvennykh matematikov [The theory of numbers and functions of Bernoulli, and its development in the works of Soviet and Russian mathematicians]. Istoriko-mat. issledovaniya 12 (1959), 59-134.
Z104,290; M24#A18; R1962,3A22

[4] Ob obobshchennykh chislakh i funktsiyakh Bernulli [On generalized numbers and functions of Bernoulli] (Ukrainian). Nauchn. zap. Poltavsk. pedagogichesk. instituta, fiz.-mat. ser. 13 (1963), no. 2, 3-21.
R1964,6A30

[5] Prilozhenie chisel Bernulli k teorii chisel [Application of Bernoulli numbers in number theory] (Ukrainian). Nauchn. zap. Poltavsk. pedagogichesk. instituta, fiz.-mat. ser. 13 (1963), no. 2, 22-31.
R1964,6A31

LIM PIL-SANG: see KIM HAN SOO, LIM PIL-SANG, KIM TAEKYUN

LINDELÖF E.,
[1] Le calcul des résidus et ses applications à la théorie des fonctions. Gautier-Villars, Paris, 1905. 141 pp.
J36.468

LIPSCHITZ R.,
[1] Über die Darstellung gewisser Functionen durch die Eulersche Summenformel, J. Reine Angew. Math., 56 (1859), 11-26.

[2] Beiträge zu der Kenntniss der Bernouillischen Zahlen, J. Reine Angew. Math., 96 (1884), 1-16.
J16.152

[3] Über Eigenschaften der Bernoullischen Zahlen, Deutsch. Natf. Ber., 1883, 56-57.

[4] Sur la représentation asymptotique de la valeur numérique ou de la partie entière des nombres de Bernoulli, Bull. Sci. Math. (2), 10 (1886), no. 1, 135-144.
J18.225

LIU BO LIAN,
[1] The sum of $k$th powers of the first $n$ integers. Dongbei Shuxue, 6 (1990), no. 3, 291-296.
Z741.11013; M91k:11020

LIU GUO DONG,
[1] $n$-variable Euler numbers and polynomials, and $n$-variable Bernoulli numbers and polynomials. (Chinese), J. Math. (Wuhan) 17 (1997), no. 3, 352-358.
M99k:11031

[2] Higher-order multivariable Euler's polynomial and higher-order multivariable Bernoulli's polynomial, Appl. Math. Mech. (English Ed.) 19 (1998), no. 9, 895-906; translated from Appl. Math. Mech. 19 (1998), no. 9, 827-836 (Chinese).
M2000c:11028

[3] Generalized Euler-Bernoulli polynomials of order $n$. (Chinese), Math. Practice Theory 29 (1999), no. 3, 5-10.

LJUNGGREN W.,
[1] Aritmetiske egenskaper ved de Bernoulliske tall [Arithmetical properties of the Bernoulli numbers], Norsk Mat. Tidsskr., 28 (1946), 33-37.
Z60,087; M8-314f

[2] A theorem on the elementary symmetric functions of the n first odd numbers, Norske Vid. Selsk. Forh., 19 (1946), no. 5, 14-17.
Z60,85; M8-368g

[3] Sur un théorème de M. E. Jacobsthal, Avhdl. Norske Vid. Akad. Oslo, 1 (1947), no. 5, 1-14.
Z30.198; M9-568e

LOBACHEVSKII N.I.,
[1] Sposob uverit'sya v ischeznovenii strok i priblizhat'sya k znacheniyu funktsij ot ves'ma bol'shikh chisel [A method of convincing oneself of the vanishing of series and approximating the value of functions from very large numbers]. (1835). Sobranie sochinenij [Collected Works], Vol. 5, Moskva, 1951, 81-162.
M13-612n

LOEB D.E.,
[1] The iterated logarithmic algebra, Adv. Math., 86 (1991), no. 2, 155-234.
Z816.05011; M92g:05022

[2] The iterated logarithmic algebra. II. Sheffer sequences. J. Math. Anal. Appl., 156 (1991), no. 1, 172-183.
Z742.05010; M92d:05013

LÖH G.: see KELLER W., LÖH G.

LOHNE J.,
[1] Potenssummer av de naturlige tall [Sums of powers of natural numbers], Nordisk Mat. Tidsskrift, 6 (1958), 155-158, 182.

LONGCHAMPS G.,
[1] Sur les nombres de Bernoulli, Ann. de l'Ecole Normale (2), 8 (1879), 55-80.
J11.185

LÓPEZ J.L.; TEMME N.M.,
[1] Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions. Stud. Appl. Math. 103 (1999), no. 3, 241-258.

[2] Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials, generalized Bernoulli, Euler, Bessel, and Buchholz polynomials, J. Math. Anal. Appl. 239 (1999), no. 2, 457-477.

LOUBOUTIN ST.,
[1] Détermination des corps quartiques cycliques totalement imaginaires à groupe des classes d'idéaux d'exposant $\leq 2$. Manuscr. Math., 77 (1992), no. 4, 385-404.
Z799.11046; M93m:11114

[2] Computation of relative class numbers of imaginary abelian number fields, Experiment. Math. 7 (1998), no. 4, 293-303.

LOVELACE, Augusta Ada, Countess of: see KING, AUGUSTA ADA

LU HONG-WEN,
[1] Congruences for the class number of quadratic fields, Abh. Math. Sem. Univ. Hamburg, 52 (1982), 254-258.
Z495.12003; M85b:11096; R1983,12A393

LUCAS E.,
[1] Théorie nouvelle des nombres de Bernoulli et d'Euler, C.R. Acad. Sci. Paris, 83 (1876), 539-541.
J8.143

[2] Sur les rapports qui existent entre le triangle arithmétique de Pascal et les nombres de Bernoulli, Nouv. Ann. Math. (2), 15 (1876), 497-499.
J8.143

[3] Théorie nouvelle des nombres de Bernoulli et d'Euler, Annali de Math., Milano (2), 8 (1877), 56-79.
J9.187

[4] Sur les théorèmes de Binet et de Staudt concernant les nombres de Bernoulli, Nouv. Ann. Math. (2), 16 (1877), 157-160.
J9.187

[5] Sur la généralisation de deux théorèmes dus à MM. Hermite et Catalan, Nouv. Corres. Math., 3 (1877), 69-73.
J9.188

[6] On the development of $\bigl({z\over{1-e^{-z}}}\bigr)^{\alpha}$ in a series, Messeng. Math. (2), 7 (1877), 82-84.
J9.188

[7] On the successive summations of $1^m + \cdots +x^m$, Messeng. Math., 7 (1878), 84-86.
J9.177

[8] On development in series, Messeng. Math., 7 (1877), 116.
J9.314

[9] On Eulerian numbers, Messeng. Math., 7 (1877), 139-141.
J10.191

[10] Sur les congruences des nombres eulériens et les coefficients différentiels des fonctions trigonométriques suivant un module premier, Bull. Soc. Math. France, 6 (1878), 49-54.
J10.139

[11] Sur les développements en séries, Bull. Soc. Math. France, 6 (1878), 57-68.
J10.191

[12] Sur les nouvelles formules de MM. Seidel et Stern, concernant les nombres de Bernoulli, Bull. Soc. Math. France, 8 (1880), 169-173.
J12.194

[13] Démonstration du théorème de Clausen et de Staudt concernant les nombres de Bernoulli, Mathesis, 3 (1883), 25-28.
J15.205

[14] Démonstration du théorème de Clausen et de Staudt, sur les nombres de Bernoulli, Bull. Soc. Math. France, 11 (1883), 69-72.
J15.205

[15] Théorie des nombres, Paris, (1891), t.1.
J23.174

[16] Sur les théorèmes énoncés par Fermat, Euler, Wilson, Staudt et Clausen, Mathesis (2), 1 (1891), 5-12.
J23.197

LUCAS E., CATALAN E.,
[1] Sur les calcul symbolique des nombres de Bernoulli, Nouv. Corres. Math., 2 (1876), 328-338.
J8.150

LUCHT L.G.,
[1] Arithmetical aspects of certain functional equations, Acta Arith. 82 (1997), no. 3, 257-277.
Z980.02698

LUCK J.-M.: see WALDSCHMIDT M. et al.

LUNDELL A.T.,
[1] On the denominator of generalized Bernoulli numbers, J. Number Theory, 26 (1987), 79-88.
Z621.10010; M88d:11020; R1987,10A64

LURSMANASHVILI A.P.,
[1] On the number of lattice points in multidimensional spheres. (Russian) Akad. Nauk. Gruzin. SSR. Trudy Tbiliss. Mat. Inst. Razmadze, 19 (1953), 79-120.
Z52,42; M16-451b; R1954,3210

LYAKHOVITSKII V.N.,
[1] A relation for Bernoulli numbers. (Russian) Mat. Zametki, 1 (1967), 633-644.
Z174,74; M35#6613; R1967,11V243

LYCHE R.T.: see TAMBS LYCHE R.


MACLAURIN C.,
[1] A treatise of fluxions, Edinburgh, 1742.

MACLEOD R.A.,
[1] Fractional part sums and divisor functions, J. Number Theory 14 (1982), no. 2, 185-227.
Z481.10044; M83m:10080

[2] A curious identity for the Möbius function, Utilitas Math., 46 (1994), 91-95.
Z821.11053; M95g:11002

MACLEOD R.A.: see LEEMING D.J., MACLEOD R.A.

MADHEKAR H.C.,
[1] Some results in unified form for classes of generalized Bernoulli, Euler, and related polynomials, J. Indian Acad. Math., 4 (1982), no. 2, 104-112.
Z516.33010; M84e:33021

MADSEN I.: see BENTSEN S., MADSEN I.

MAEDA Y.,
[1] Generalized Bernoulli numbers and congruence of modular forms, Duke Math. J., 57 (1988), no. 2, 673-696.
Z664.10012; M89m:11042; R1989,6A92

MAESS G.,
[1] Vorlesungen über numerische Mathematik. II. Analysis. Akademie-Verlag, Berlin, 1988, and Birkhäuser Verlag Basel-Boston, 1988, 327 pp.
Z644.65001; M91a:65003; R1989.6G14K

MAGNUS W.: see ERDÉLYI A., MAGNUS W., OBERHETTINGER F., TRICOMI F.

MAHON BR. J.M., HORADAM A.F.,
[1] Infinite series summation involving reciprocals of Pell polynomials. In: Fibonacci Numbers and Their Applications (A.N. Philippou et al., Eds.), D. Reidel Publ. Co., Dordrecht, 1986, 163-180.
Z592.10010; M88b:11011

MAIER W.,
[1] Euler-Bernoullische Reihen, Math. Z., 30 (1929), 53-78.
J55.782

[2] Bernoullische Polynome und elliptische Funktionen. J. Reine Angew. Math., 164 (1931), 85-111.
J57.441; Z1,282

MAINZER K.: see EBBINGHAUS H.-D. et al.

MALAISE J.,
[1] Sur une formule d'approximation pour les nombres de Bernoulli très grands, Nouv. Ann. Math. (4), 14 (1914), 174-179.
J45.677

[2] Sur la formule $hU^{\prime}_x = \Delta U_x - {h\over 2} {\Delta} U^{\prime}_x + B_1{h^2\over 2} {\Delta} U^{\prime \prime}_x$ etc., J. Reine Angew. Math., 35 (1847), 55-82.

MALLET C.-A.,
[1] Calcul des dalles encastrées. Application des polynomes de Bernoulli, C. R. Acad. Sci. Paris A, 268 (1969), 974-977.
Z181,526

MALLOCH L.,
[1] Bernoulli-Padé numbers and polynomials. M.Sc. thesis, Dalhousie University, Halifax, Nova Scotia, 1996. 80pp.

MALMSTÉN C.J.,
[1] Note sur l'integrale finite $\Sigma e^x y$, Arch. Math. und Physik, 6 (1845), 41-45.

MAMBRIANI A.,
[1] Saggio di una nuova trattazione dei numeri i dei polinomi di Bernoulli e di Euler. Mem. R. Accad. Italia Mat., 3 (1932), no.4, 1-36.
J58.I.376; Z6.051

MANGEOT S.,
[1] Sur les nombres de Bernoulli, Ann. Fac. Sci., Marseille, 2 (1892), 63-65.

MANIN Yu.I.,
[1] Non-archimedean integration and p-adic Jaquet-Langlands L-functions. (Russian) Uspehi. Mat. Nauk., 31 (1976), no. 1(187), 5-54.
Z348.12016; M54#5194; R1976,8A478

MANIN Yu.I., PANCHISHKIN A.A.,
[1] An introduction to the theory of numbers. (Russian) Current problems in mathematics. Fundamental directions, Vol. 49, Itogi Nauki i Tekhniki., Akad. Nauk. SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform, Moscow, 1990, 5-348.
Z732.11002; M91j:11001b

MARKETT C.: see BUTZER P.L., MARKEETT C., SCHMIDT M.

MARKOV A.A.,
[1] Ischislenie konechnykh raznostej, Otdel 2, Uravnenie v konechnykh raznostyakh i summirovanie [The calculus of finite differences. The equation in finite differences and summation]. Sankt-Peterburg, 1891.
J23.347

[3] (A.A. Markoff) Differenzenrechnung. Teubner, Leipzig, 1896.
J27.261

MARSAGLIA G., MARSAGLIA J.C.W.,
[1] A new derivation of Stirling's approximation to $n!$, Amer. Math. Monthly, 97 (1990), no. 9, 826-829. (See also: N. Grossman, Letter to the Editor, Amer. Math. Monthly, 98 (1991), no. 3, 233.)
Z786.05007; M92b:41049

MARTINET J.,
[1] Sur l'ouvrage de Hasse "Über die Klassenzahl Abelscher Zahlkörper". Séminaire de Théorie des nombres. Univ. Bordeaux I, année 1982-83 (1983), exp. no. 4, 15 pp.
Z526.12003; M85m:11071

MATHAI A.M., PEDERZOLI G.,
[1] A direct statistical technique of obtaining some summation formulae for Bernoulli polynomials and representations of certain algebraic functions, Metron, 43 (1985), no. 3-4, 157-166.
Z598.33001; M87j:33001

MATIYASEVICH Yu.V.,
[1] Hilbert's tenth problem. Foundations of Computing Series. MIT Press, Cambridge, MA, 1993. xxiv+264pp.
Z790.03009; M94m:03002b

MATSUMOTO K.: see KATSURADA M., MATSUMOTO K.

MATSUOKA Y.,
[1] On the values of a certain Dirichlet series at rational integers, Tokyo J. Math., 5 (1982), no. 2, 399-403.
Z505.10020; M84d:10046; R1983,8A117

[2] A table of the explicit formulas for the sums of powers $S_p(n) = \sum_{k=1}^n k^p$ for $p=62(1)99$. Rep. Fac. Sci. Kogashima Univ. Math. Phys. Chem., 22 (1990), 73-132.
Z682.10012; M91k:11021

[3]A table of the explicit formulas for the sums of powers $S_p(n) = \sum_{k=1}^n k^p$ for $p=100(1)119$. Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem., 23 (1990), 41-100.
Z731.11013

MATSUOKA Y.: see also ORIGUCHI T., KIRIYAMA H., MATSUOKA Y.

MATTER K.,
[1] Die den Bernoullischen Zahlen analogen Zahlen im Körper der 3. Einheitswurzeln, Diss., Zürch, 1900. Zürch. Naturf. Ges., 45, 238-269.
J31.204

MATTICS L.E.: see GESSEL I., MATTICS L.E.

MAZUR B.,
[1] Review of Kummer's Collected Papers, Vols. I and II, ed. by A. Weil, Bull. Amer. Math. Soc., 83 (1977), no. 5, 976-988.

MAZUR B., WILES A.,
[1] Analogues between function fields and number fields, Amer. J. Math., 105 (1983), no. 2, 507-521.
Z531.12015; M84g:12003

[2] Class fields of abelian extensions of Q, Invent. Math., 76 (1984), no. 2, 179-330.
Z545.12005; M85m:11069; R1985,2A351

McCALLUM W.G.,
[1] On the Shafarevich-Tate group of the Jacobian of a quotient of the Fermat curve, Invent. Math., 93 (1988), no. 3, 637-666.
Z661.14033; M90b:11059

[2] The arithmetic of Fermat curves. Math. Ann., 294 (1992), no.3, 503-511.
Z766.14013; M93j:11037

McCARTHY P.J.,
[1] Some irreducibility theorems for Bernoulli polynomials of higher order, Duke Math. J., 27 (1960), 313-318.
Z178,373; M22#5613; R1961,6A137

[2] Irreducibility of certain Bernoulli polynomials, Amer. Math. Monthly, 68 (1961), 352-353.
Z98,248; M23#A1625; R1962,5A161

[3] Irreducibility of Bernoulli polynomials of higher order, Canad. J. Math., 14 (1962), 565-567.
Z118,260; M25#4150; R1963,7B63

McCLENON R.B.,
[1] Bernoulli numbers, Proc. Iowa Acad. Sci., 57 (1950), 315-319.
M13-13f

McINTOSH R.J.,
[1] A necessary and sufficient condition for the primality of Fermat numbers, Amer. Math. Monthly, 90 (1983), no. 2, 98-99.
Z513.10012; M85c:11022; R1983,3A111

[2] On the converse of Wolstenholme's theorem. Acta Arith. 71 (1995), no. 4, 381-389.
Z829.11003; M96h:11002; R1996,5A120

[3] Franel integrals of order four, J. Austral. Math. Soc. Ser. A, 60 (1996), no. 2, 192-203.
Z855.11020; M96j:11055; R1997,5A35

MELHAM R.S., SHANNON A.G.,
[1] Some infinite series summations using power series evaluated at a matrix. Fibonacci Quart., 33 (1995), no. 1, 13-20.
Z826.11007; M95k:11025

MERCIER A.,
[1] Sums containing the fractional parts of numbers, Rocky Mountain J. Math., 15 (1985), no. 2, 513-520.
Z588.10044; M87e:11011

MESSICK C.A.,
[1] A new method of determining Bernoulli's numbers, Amer. Math. Monthly, 33 (1926), 214-217.
J52.355

METSÄNKYLÄ T.,
[1] A congruence for the class number of a cyclic field, Ann. Acad. Sci. Fennicae, Ser. AI, Math., (1970), no. 472, 1-11.
Z194,352; M42#3057; R1971,4A319

[2] Note on the distribution of irregular primes, Ann. Acad. Sci. Fennicae, Ser. AI, Math., (1971), no. 492, 1-7.
Z208,55; M43#168; R1971,9A100

[3] A class number congruence for cyclotomic fields and their subfields, Acta Arith., 23 (1973), 107-116.
Z233.12004; M48#11046; R1974,1A176

[4] On the cyclotomic invariants of Iwasawa, Math. Scand., 37 (1975), 61-75.
Z314.12004; M52#10677; R1976,11A432

[5] On the Iwasawa invariants of imaginary abelian fields, Ann. Acad. Sci. Fennicae, Ser. AI, 1 (1975), 343-353.
Z323.12010; M53#347; R1976,11A426

[6] Distribution of irregular prime numbers, J. Reine Angew. Math., 282 (1976), 126-130.
Z327.10041; M53#2865; R1976,10A99

[7] Note on certain congruences for generalized Bernoulli numbers, Arch. Math. (Basel), 30 (1978), 595-598.
Z(371.12003),378.12001; M58#16602; R1978,12A180

[8] Iwasawa invariants and Kummer congruences, J. Number Theory, 10 (1978), 501-522.
Z(381.12009),388.12006; M80d:12007; R1978,6A302

[9] An upper bound for the $\lambda$-invariant of imaginary abelian fields, Math. Ann., 264 (1983), 5-8.
Z(497.12002),505.12005; M85a:11019; R1984,1A283

[10] Maillet's matrix and irregular primes, Ann. Univ. Turku., Ser. AI, (1984), no. 186, 72-79.
Z531.12003; M85j:11145; R1985,1A213

[11] The Voronoi congruence for Bernoulli numbers. The Very Knowledge of Coding. Studies in honour of Aimo Tietäväinen, Turun yliopiston offsetpaino-Turku, 1987, 112-119.
Z632.10006; M88m:11010; R1988,3A414

[12] The index of irregularity of primes, Expositiones Math., 5 (1987), 143-156.
Z608.12004; M88f:11011; R1987,9A80

[13] A simple method for estimating the Iwasawa $\lambda$-invariant, J. Number Theory, 27 (1987), no. 1, 1-6.
Z612.12005; M88m:11091; R1988,3A414

[14] Cyclotomic fields, irregular primes, and supercomputing (Finnish). Arkhimedes, 45 (1993), no. 2, 116-128.
Z776.14013; M94g:11094; R1994,2A15

[15] An application of the $p$-adic class number formula, Manuscr. Math., 93 (1997), no. 4,481-498.
Z886.11061; M98m:11118

[16] Some divisibility results for the cyclotomic class numbers, Tatra Mountains Math. Publ. 11 (1997), 56-68.

[17] Letter to the editor. Comment on: "On Demjanenko's matrix and Maillet's determinant for imaginary abelian number fields" [J. Number Theory 60 (1996), no. 1, 70-79] by H. Tsumura. J. Number Theory 64 (1997), no. 1, 162-163.

METSÄNKYLÄ T.: see also ERNVALL R., METSÄNKYLÄ T.

METSÄNKYLÄ T.: see also BUHLER J.P. et al

MEURMAN A.: see ALMKVIST G., MEURMAN A.

MEYER C.,
[1] Über die Bildung von elementar-arithmetischen Klasseninvarianten in reell-quadratischen Zahlkörpern. Algebraische Zahlentheorie (Ber. Tagung Math. Forschungsinst. Oberwolfach, 1964) Bibliographisches Institut, Mannheim, 1967, 165-215.
Z122,52; M38#2121; R1965,5A146

MEYER G.F.,
[1] Über Bernoulli'sche Zahlen, Diss. Göttingen, 1859, 56pp.

[2] Einige Beiträge zur Theorie der Bernoullischen Zahlen und der Secantencoefficienten, Arch. für Math. und Phys., 35 (1860), 449-474.

[3] Verschiedene arithmetische Sätze, Arch. für Math. und Phys., 38 (1862), 241-246.

[4] Vorlessungen über die Theorie der bestimmten Integrale zwischen reellen Grenzen, Leipzig, 1871, sects. 53, 54.
J3.125

MEYER J.R.,
[1] Une conjecture de Chowla et Walum, J. Number Theory, 21 (1985), no. 3, 245-255.
Z568.10023; M87a:11089; R1986,5A137

MEYER W., VON RANDOW R.,
[1] Ein Würfelschnittproblem und Bernoullische Zahlen, Math. Ann., 193 (1971), 315-321.
Z209,344; M45#2569; R1972,4V308

MIKELADZE SH. E.,
[1] Numerical integration. (Russian) Uspekhi Matem. Nauk (N.S.), 3 (1948), 3-88.
Z41,444; M10-575g

[2] Numerical methods of mathematical analysis. (Russian) Gosudarstv. Izdat. Tekhn.-Teor. Lit., Moscow, 1953, 527 pp.
Z52,349; M16-627c; R1955,1974K

MIKI H.,
[1] A relation between Bernoulli numbers, J. Number Theory, 10 (1978), no. 3, 297-302.
Z379.10007; M80a:10024; R1979,2A109

[2] On the congruence for Gauss sums and its applications. Théorie des nombres (Quebec, PQ, 1987), 633-641, deGruyter, Berlin, 1989.
Z715.11041; M91h:11083

[3] On the conductor of the Jacobi sum Hecke character. Comp. Math., 92 (1994), no. 1, 23-41.
Z798.11049; M95i:11131

MIKOLÁS M.,
[1] Sur une extension de la formule d'Euler-Maclaurin, se rapportant à des intégrales curvilignes complexes. C. R. du I Congr. Math. Hongr., (1950), 519-538, 541-550. Akadémiai Kiadó, Budapest, 1952.
Z49.53; M14-1073g

[2] Über die Beziehung zwischen der Gammafunktion und den trigonometrischen Funktionen. Acta Math. Acad. Sci. Hungar., 4 (1953), no. 1-2, 143-157.
Z51.52; M15-525d; R1954,2989

[3] Zur Theorie der Gammafunktion, der Riemannschen Zetafunktion und verwandter Funktionen, I. Acta Math. Acad. Sci. Hungar., 6 (1955), no. 3-4, 381-438.
Z68.283; M19-132e; R1957,1568

[4] Integral formulae of arithmetical characteristics relating to the zeta-function of Hurwitz. Publ. Math., Debrecen, 5 (1957), no. 1-2, 44-53.
Z81.274; M19-731; R1958,6429

[5] Über gewisse Lambertsche Reihen. I. Verallgemeinerung der Modulfunktion $\eta(\tau)$ und ihrer Dedekindschen Transformationsformel. Math. Z., 68 (1957), no. 1, 100-110.
Z78.70; M19-943b; R1959,2305

[6] Über die Charakterisierung der Hurwitzschen Zetafunktion mittels Funktionalgleichungen, Acta Sci. Math. Szeged, 19 (1958), no. 3-4, 247-250.
Z87,74; M21#1953; R1960,93

[7] On a problem of Hardy and Littlewood in the theory of Diophantine approximations. Publ. Math., Debrecen, 7 (1960), no. 4, 158-180.
Z96,261; M22#10978; R1961,10A135

[8] Einige neuere Aspekte und analytische-technische Anwendungen Diophantischer Approximationen. Result. Math., 18 (1990), no. 3/4, 298-305.
Z716.11032; M92e:11072

MILLAR J., SLOANE N.J.A., YOUNG N.E.,
[1] A new operation on sequences: the boustrophedon transform, J. Combin. Theory Ser. A 76 (1996), no. 1, 44--54.
Z858.05007; M97e:05020

MILLER H.,
[1] Universal Bernoulli numbers and the $S^1$-transfer. Current Trends in Algebraic Topology, Part 2 (London, Ont., 1981), Canad. Math. Soc. Conf. Proc., Vol. 2, Amer. Math. Soc., Providence, R.I., 1982, pp. 437-449.
Z544.55005; M85b:55029

MILLER J.B.,
[1] The Euler-Maclaurin sum formula for an inner derivation, Aequationes Math., 25 (1982), no. 1, 42-51.
Z519.47022; M85b:46057; R1984,2B1093

[2] Series like Taylor's series, Aequationes Math., 26 (1983), no. 2-3, 208-220.
Z562.40001; M86a:30081; R1985,2B915

[3] The Euler-Maclaurin formula generated by a summation operator, Proc. Roy. Soc. Edinburgh Sect. A, 95 (1983), no. 3-4, 285-300.
Z527.47024; M85f:47018; R1984,6B1042

[4] The Euler-Maclaurin sum formula for a closed derivation, J. Austral. Math. Soc. Ser. A, 37 (1984), no. 1, 128-138.
Z545.47022; M86d:47043; R1985,3B1003

[5] The standard summation operator, The Euler-Maclaurin sum formula, and the Laplace transformation, J. Austr. Math. Soc. Ser. A, 39 (1985), no. 3, 367-390.
Z589.65003; M86j:65011; R1986,6B1218

[6] The operator remainder in the Euler-Maclaurin formula, Aequationes Math., 28 (1985), no. 1-2, 64-68.
Z558.41031; M86m:41040; R1985,7B948

MILLER J.C.P.: see FLETCHER A. et al.

MILLS S.,
[1] The independent derivations by Leonhard Euler and Colin Maclaurin of the Euler-Maclaurin summation formula, Arch. Hist. Exact Sci., 33 (1985), no. 1-3, 1-13.
Z607.01013; M86i:01025; R1985,12A8

MILNE-THOMSON L.M.,
[1] The Calculus of Finite Differences. Macmillan, London, 1933, xix + 558 pp.
Z8,018; J59.II.1111

MILNOR J.,
[1] On polylogarithms, Hurwitz zeta functions, and the Kubert identities. L'Enseign. Math., 29 (1983), no. 3-4, 281-322.
Z557.10031; M86d:11007; R1984,5A117

MILNOR J.W., STACHEFF J.,
[1] Characteristic classes. Annals of Math. Stud., No. 76, Princeton University Press, Princeton, 1974.
Z298.57008; M55#13428; R1975,3A611K

MILNOR J.W.: see also KERVAIRE M.A., MILNOR J.W.

MILOSEVIC-RAKOCEVIC K.,
[1] Staudt-Clausenova teorema, Mat. Bibl., 22 (1962), 71-79.
R1964,2A176

[2] Prilozi teoriji i praksi Bernoullievih polinoma i brojeva, (Serbo-Croatian), [Applications of the theory and practice of Bernoulli polynomials and numbers], Matematicki Institut u Beogradu, Belgrade, 1963, 143 pp.
Z193,363; M31#3635; R1964,2A176

MINÁC J.,
[1] A remark on the values of the Riemann zeta function, Exposition. Math., 12 (1994), no. 5, 459-462.
Z812.11051; M96a:11082

MINOLI D.,
[1] Asymptotic form for generalized factorial, Rev. Colombiana Mat., 11 (1977), no. 1-4, 59-75.
Z445.05007; M58#27853; R1979,4B1

[2] Some results for modified Bernoulli polynomials, Notices Amer. Math. Soc., 26 (1979), A-613.

[3] Inductive formulae for general sum operations, Math. Comp., 34 (1980), no. 150, 543-545.
Z424.40003; M81g:65002; R191980,11A65

MIRIMANOFF D.,
[1] L'equation indéterminée $x^l+y^l+z^l=0$ et le critérium de Kummer, J. Reine Angew. Math., 128 (1905), 45-68.
J35.216

[2] Sur le dernier théorème de Fermat et le critérium de M. A. Wieferich, Enseign. Math., 11 (1909), 455-459.
J40.257

[3] Sur le dernier théorème de Fermat, J. Reine Angew. Math., 139 (1910), 309-324.
J41.236

[4] Sur les nombres de Bernoulli, Enseign. Math., 36 (1937), 228-235.
J63.106; Z17,062

MISHRA S.S.: see SHUKLA R.N., MISHRA S.S.

MISHRA S.S.: see SINGH S.N., MISHRA S.S.

MISON K.,
[1] Stanoveni Bernoulliho cisel. Soucet posloupnosti bez uziti diferencnich posloupnosti [Definition of the Bernoulli numbers. Sum of an arithmetic series without use of difference series], (Czech), Casopis Pest. Mat., 76 (1951), 199-200.
M14-4786

MISRA S.S., SHUKLA R.N.,
[1] Some properties of multivariate Bernoulli polynomials of the second kind (Hindi. English and Hindi summaries). Vijnana Parishad Anusandhan Patrika, 37 (1994), no. 2, 77-85.
M96b:11019

MITRINOVIC D.S.,
[1] Sur les nombres de Bernoulli d'ordre supérieur, Bull. Soc. Math. Phys. Serbie, 11 (1959), 23-26.
Z135,91; M32#299

[2] Sur une relation de récurrence relative aux nombres de Bernoulli d'ordre supérieur, C.R. Acad. Sci., Paris, 250 (1960), 4266-4267.
Z99,281; M22#12049; R1961,6A138

[3] Sur une formule concernant les nombres de Bernoulli d'ordre supérieur, Bull. Soc. Math. Phys. Serbie, 12 (1960), 21-23.
Z135,91; M32#1474

MITRINOVIC D.S., MITRINOVIC R.S.,
[1] Sur les nombres de Stirling et les nombres de Bernoulli d'ordre supérieur, Publ. electr. fak. Univ. Beogradu, ser. mat. i fiz., (1960), no. 43, 1-63.
Z106,32; M23#A1547; R1962,8V199

MITRINOVIC R.S.: see MITRINOVIC D.S., MITRINOVIC R.S.

MITROVIC Z.M.: see JAPIC R.R., MITROVIC Z.M.

MIYAKE T.,
[1] Modular forms. Springer-Verlag, Berlin-New York, 1989. x+335 pp.
Z701.11014; M90m:11062

MIYOSHI T.,
[1] On the Diophantine equation $x^l+y^l=cz^l$, 2, TRU Math., 2 (1966), 53-54.
Z149,288; M36#6349; R1968,4A122

MIZUMOTO S.,
[1] On integrality of certain algebraic numbers associated with modular forms, Math. Ann., 265 (1983), no. 1, 119-135.
Z578.10031; M85i:11047; R1984,3A591

[2] Congruences for eigenvalues of Hecke operators on Siegel modular forms of degree two, Math. Ann., 275 (1986), no. 1, 149-161.
Z578.10032; 588.10029; M87k:11054; R1986,12A549

[3] Integrality of critical values of triple product $L$-functions. Analytic number theory (Tokyo, 1988), 188--195, Lecture Notes in Math., 1434, Springer, Berlin, 1990.
M91j:11034

MOIVRE A. DE: see DE MOIVRE A.

MOLLAME V.,
[1] Sulla somma delle potenze simili di numeri qualunque in progressione aritmetica, esopra alcuni coefficienti analoghi ai numeri bernulliani che si presento in tale somma. Catania, Accad. Gioen. Atti 15 (1881), 261-272.

MONAGAN M.B.: see GRANVILLE A., MONAGAN M.B.

MONTGOMERY H.L.,
[1] Distribution of irregular primes, Illinois J. Math., 9 (1965), 553-558.
Z131,45; M31#5861; R1966,8A97

MORDELL L.J.,
[1] Three lectures on Fermat's last theorem. Cambridge Univ. Press, 1921. Also in: Famous problems and other monographs, Chelsea Publ. Co., New York, 1955; and in: L.J. Mordell, Two papers on number theory, VEB Deutscher Verlag der Wissenschaften, Berlin, 1972.
Z237.10016; M50#4453

[2] On the evaluation of some multiple series, J. London Math. Soc., 33 (1958), 368-371.
Z81,275; M20#6615; R1959,4426R

[3] Integral formulae of arithmetical character, J. London Math. Soc., 33 (1958), 371-375.
Z81,274; M20#6488; R1960,1286

[4] On a Pellian equation conjecture, Acta Arith., 6 (1960), 137-144.
Z93,43; M22#9470; R1961,7A121

[5] Recent work in number theory, Scripta Math., 25 (1960), 93-103.
Z109,270; M22#9471; R1961,5A107

[6] On a Pellian equation conjecture. II. J. London Math. Soc., 36 (1961), 282-288.
Z122,55; M23#A3707; R1962,5A154

[7] A Pellian equation conjecture, Second Hung. Math. Congress 1960, Budapest, 1 (1961), 1b, 24-27.

[8] Expansion of a function in a series of Bernoulli polynomials, and some other polynomials, J. Math. Anal. Appl., 15 (1966), 132-140.
Z166,70; M33#6276; R1967,3B57

[9] Expansion of a function in terms of Bernoulli polynomials, J. London Math. Soc., 41 (1966), 526-528.
Z165,70; M33#6276; R1967,9V207

[10] Diophantine equations. Pure and Appl. Math., Vol. 30, Acad. Press, London-New York, 1969, x + 312 pp., Ch. 8.
Z188.345; M40#2600; R1970,8A97K

[11] The sign of the Bernoulli numbers, Amer. Math. Monthly, 80 (1973), 547-548.
Z273.10011; M47#4918; R1974,2V418

MOREE P.,
[1] On a theorem of Carlitz - von Staudt. C. R. Math. Rep. Acad. Sci. Canada, 16 (1994), no. 4, 166-170.
Z820.11002; M95i:11002

[2] Primes in arithmetic progression having a prescribed primitive root, MPI für Math., Bonn, Preprint Ser. 1998(57).

MOREE P., TE RIELE H.J.J., URBANOWICZ J.,
[1] Divisibility properties of integers $x$, $k$ satisfying $1^k+\ldots +(x-1)^k=x^k$, Math. Comp., 63 (1994), no. 208, 799-815.
Z816.11024; M94m:11041; R1997,12A101

MORENO C.J.,
[1] The Chowla-Selberg Formula, J. Number Theory, 17 (1983), no. 2, 226-245.
Z525.12012; M85b:11034; R1984,3A569

MORI K.: see AGOH T., MORI K.

MORISHIMA T.,
[1] Über die Fermatsche Vermutung, XI, Japan J. Math., 11 (1935), 241-252.
J61.I.174; Z11,338

[2] Über die Fermatsche Vermutung, XII, Proc. Imper. Acad. Tokyo, 11 (1935), no. 8, 307-309.
J61.I.175; Z13,052

[3] On Fermat's last theorem (13th paper), Trans. Amer. Math. Soc., 72 (1952), no. 1, 67-81.
Z47,47; M13-726e

[4] On the second factor of the class number of the cyclotomic fields, J. Math. Anal. Appl., 15 (1966), 141-153.
Z139,282; M33#5607; R1967,7A146

MORO G.,
[1] L'ultimo teorema di Fermat, Riv. Mat., 1986, Suppl., 86 pp.
R1986,8A101

MOUSSA P.: see WALDSCHMIDT M. et al.

MÜLLER H.,
[1] On some congruences concerning the criteria of Kummer, Expositiones Math., 2 (1984), no. 1, 85-89.
Z525.12012; M86h:11024; R1984,10A94

MUNCH O.J.,
[1] Om Potensproduktsummer, Nordisk Mat. Tidsskrift, 7 (1959), 5-19.
Z084.26902; R1960,3178

MÜNTZ CH.-H.,
[1] Sur une propriété des polynômes de Bernoulli, C.R. Acad. Sci., Paris, 158 (1914), 1864-1866.
J45.677

MURAKAMI JUN: THANG LE THU QUAC, MURAKAMI JUN

MUSÈS C.,
[1] A closed expression for the zeta function of odd integer argument, Abstracts Amer. Math. Soc., 4 (1983), no. 5, 339.

[2] Bernoulli numbers of general index, Abstracts Amer. Math. Soc., 8 (1987), no. 1, 17.

[3] Bernoulli numbers of general index, Abstracts Amer. Math. Soc., 15 (1994), no. 1, 23.


NAGAOKA S.,
[1] $p$-adic properties of Siegel modular forms of degree $2$, Nagoya Math. J. 71 (1978), 43-60.
Z393.10029; M80g:10027

[2] Some congruence property of modular forms, Manuscripta Math. 94 (1997), no. 2, 253-265.
Z980.18769; M98g:11054

NAGASAKA CH.,
[1] Eichler integrals and generalized Dedekind sums, Mém. Fac. Sci., Kyushu Univ., Ser. A, 37 (1983), no. 1, 35-43.
Z512.10030; M84f:10032; R1983,10A96

[2] On generalized Dedekind sums attached to Dirichlet characters, J. Number Theory, 19 (1984), no. 3, 374-385.
Z551.10022; M86f:11035; R1985,5A329

[3] Dedekind type sums and Hecke operators. Acta Arith. 44 (1984), no. 3, 207-214.
Z512.10007, 543.10013; M86i:11020; R1985,7A158

NÄGELSBACH H.,
[1] Zur independenten Darstellung der Bernoulli'schen Zahlen, Zeit. für Math. und Phys., 19 (1874), 219-234.
J6.140

NAKAGOSHI N.,
[1] On the unramified extension of the prime cyclotomic number field and its quadratic extension, Nagoya Math. J., 115 (1989), 151-164.
Z(659.12007)673.12002; M90m:11159; R1990,6A301

[2] On the unramified Kummer extensions of quadratic extensions of the prime cyclotomic number field, Arch. Math. 57 (1991), no. 6, 566-570.
Z728.11056; M93b:11139

NAKAJIMA MASUMI,
[1] The Taylor coefficients of ${\zeta}(s)$, $(s-1){\zeta}(s)$ and $(z/(1-z)){\zeta}(1/(1-z))$, Math. J. Okayama Univ., 29 (1987), 207-219 (1988).
Z641.10030; M89f:11120; R1988,10A116

NAKAJIMA SHOICHI,
[1] On Gauss sum characters of finite groups and generalized Bernoulli numbers. Les Dix-huitièmes Journées Arithmétiques (Bordeaux, 1993). J. Théor. Nombres Bordeaux 7 (1995), no. 1, 143-154.
Z848.11052; M97g:11087

NAKAZATO H.,
[1] A remark on Ribet's theorem, Proc. Japan Acad., Ser. A, 56 (1980), no. 4, 192-195.
Z453.12001; M81g:12007

[2] The q-analogue of the p-adic gamma-function, Kotai Math. J., 11 (1988), no. 1, 141-153.
Z664.12015; M89e:11075; R1988,10A314

NAMIAS V.,
[1] A simple derivation of Stirling's asymptotic series, Amer. Math. Monthly, 93 (1986), no. 1, 25-29.
Z615.05010; M87i:05018; R1986,8B20

NARISHKINA E.A.,
[1] On the analogue of Bernoulli numbers in quadratic fields, Proc. Intern. Math. Congress, Toronto 1924, Reprinted 1967, v.1, 299-307. (This report at the Congress was read by V.A.Steklov.)

[2] O chislakh analogichnykh chislam Bernulli, v odnoklassovykh kvadratichnykh oblastyakh otritsatel'nogo diskriminanta [On numbers analogous to Bernoulli numbers in one-classed quadratic fields of a negative discriminant]. Izv. Rossijsk. Akad. Nauk, Ser. VI, 19 (1925), 145-176, 287-314.
J51.154

NARKIEWICZ W.,
[1] Class number and factorization in quadratic number fields, Colloq. Math., 17 (1967), 167-190.
Z153,77; M36#3750; R1968,8A339

[2] Elementary and analytic theory of algebraic numbers, Warszawa, 1974. (Second edition: PWN-Polish Scientific Publishers, Warszawa, 1990. xiii + 746 pp.)
Z276.12002; M50#268; R1974,10A321K

NATH B.,
[1] A generalization of Bernoulli numbers and polynomials, Ganita, 19 (1968), no. 1, 9-12.
Z226.10015; M45#3812

NEGGERS J.: see AINSWORTH O.R., NEGGERS J.

NEKOVÁR J.,
[1] Iwasawa's main conjecture. (A survey). Acta Math. Univ. Comenian., 50/51 (1987), 203-215.
Z675.12001; M90d:11119; R1989,10A322

NEUKIRCH J.,
[1] The Beilinson conjecture for algebraic number fields. In: Beilinson's conjecture on special values of L-functions, pp. 193-247, Perspect. Math., 4, Academic Press, Boston, 1988.
Z651.12009; M90f:11042; R1989,10A322

NEUKIRCH J.: see also EBBINGHAUS H.-D. et al.

NEUMAN C.P., SCHONBACH D.I.,
[1] Evaluation of sums of convolved powers using Bernoulli numbers, SIAM Review, 19 (1977), no. 1, 90-99.
Z355.65002; M55#1698; R1977,9B13

NGUYEN THI TINH: see TUAN VU KIM, NGUYEN THI TINH

NICOL C.A.: see SELFRIDGE J.L., NICOL C.A., VANDIVER H.S.

NIEDERHAUSEN H.,
[1] Factorials and Stirling numbers in the algebra of formal Laurent series. Discrete Math., 90 (1991), no.1, 53-62.
Z751.11013; M92j:05012; R1991,10V243

[2] Factorials and Stirling numbers in the algebra of formal Laurent series. II. $z^a-z^b=t$. Discrete Math., 132 (1994), no. 1-3, 197-213.
Z805.05006; M95k:05014

NIELAND L.W.,
[1] Over $\sum_{n=1}^m {1\over n^{2h}}$ en $\sum_{n=1}^\infty {1 \over n^{2h}} = \zeta(2h).$ Nieuw. Arch. Wisk (2), 16 (1929/30), no. 1, 1-13.
J55.130

NIELSEN N.,
[1] Handbuch der Theorie der Gammafunktion, Leipzig, 1906.
J37.450

[2] Note sur les fonctions de Bernoulli (Extrait d'une lettre à F.G. Teixeira), Ann. Ac. Pol. Porto, 6 (1911), 5-11.
J42.460

[3] Note sur les polynômes parfaits, Nieuw Arch. Wisk. (2), 10 (1912), 100-106.
J43.242

[4] Sur les transcendentes élémentaires et les nombres de Bernoulli et d'Euler, Annali di Mat. (3), 19 (1912), 179-204.
J43.532

[5] Recherches sur les nombres de Bernoulli, Kgl. Danske Videnskab. Selskabs Skrifter, Nat. og Mathem. Afdeling, 10 (1913), 283-362.
J44.398

[6] Recherches sur les suites régulières et les nombres de Bernoulli et d'Euler, Annali di Mat. (3), 22 (1913), 71-115.
J44.319

[7] Verkürzte Rekursionsformeln für Bernoullische und Eulersche Zahlen, Abh. Königl. Sächs. Ges. Wiss. Leipzig, 65 (1913), 3-26.
J44.514

[8] Sur les fonctions de Bernoulli et des sommes de puissances numériques, Nieuw. Arch. Wisk. (2), 10 (1913), 396-415.
J44.514

[9] Elementære Beviser for Sætninger af v. Staudt og Stern verdrørende de Bernoulliske Tal, Nyt Tidskr. Mat., 25 (1914), 19-23.
J45.1257

[10] Sur le théorème de v. Staudt et de Clausen relatif aux nombres de Bernoulli, Annali di Mat. (3), Milano, 22 (1914), 249-261.
J45.302

[11] Recherches sur les résidus quadratiques et sur quotients de Fermat, Ann. de l'Ecole Normale (3), 31 (1914), 161-204.
J45.323

[12] Note sur une théorie élémentaire des nombres de Bernoulli et Euler, Arch. för Math., Astr. och Fys., 9 (1914), no. 24, 1-15.
J45.677

[13] Über die von A. v. Ettingshausen entdeckten verkürzten Rekursionsformeln für die Bernoullischen Zahlen, Monatsh. Math., 25 (1914), 152-162.
J45.678

[14] Über die Verallgemeinerungen der von A. v. Ettingshausen entdeckten verkürzten Rekursionsformeln für die Bernoullischen Zahlen, Monatsh. Math., 25 (1914), 328-336.
J45.679

[15] Note sur les polynômes réguliers et sur leur application dans la théorie des nombres, Overs. Danske vidensk. Selsk. Förh., (1915), 171-180.
J45.326

[16] Sur les nombres de Bernoulli et leur application dans la théorie des nombres, Overs. Danske Vidensk. Selsk. Förh., (1915), no. 6, 509-524.
J45.303

[17] Recherches sur les fonctions de Bernoulli, Mém. Acad. R. Copenhagen (7), 12 (1915), 55-102.
J45.677

[18] Traité élémentaire des nombres de Bernoulli, Gauthier-Villars, Paris, 1923.
J49.99

[19] Note sur les séries de fonctions bernoulliens. Math. Ann., 59 (1904), no. 1/2, 103-109.
J35.448

[20] Sur les séries de fonctions de Stirling. Annali di. Mat. pura ed appl. (3), 12 (1905), 101-112.
J36.500

[21] Note sur les fonctions de Bernoulli et leur analogie aux factorielles ordinaires. Oversigt Kongl. Dansk. Vidensk. Selsk. Forhandl., no. 4, 1916, 191-201.
J46.567

[22] Note sur les nombres de Bernoulli et d'Euler. Nyt Tidskr. Mat., B28 (1917), 1-7.
J46.568

[23] Recherches sur les polynômes de Stirling. Copenhagen, 1920, 106pp.

NIEMEYER H.,
[1] Bernoullische Zahlen in imaginär-quadratischen Zahlkörpen. Staatsexamensarbeit, Hamburg 1966.

NIKULIN M.: see VOINOV V., NIKULIN M.

NISHIZAWA M.: see UENO K., NISHIZAWA M.

NÖRLUND N.E.,
[1] Sur les polynômes de Bernoulli, C.R. Acad. Sci., Paris, 169 (1919), 521-524.
J47.216

[2] Mémoire sur les polynômes de Bernoulli, Acta Math., 43 (1922), 121-196.
J47.216

[3] Remarques diverses sur le calcul aux différences finies, J. de Math. Pures Appl. (9), 2 (1923), 193-214.
J49.324

[4] Sur certaines équations aux différences finies, Trans. Amer. Math. Soc., 25 (1923), 13-48.
J49.324

[5] Vorlesungen über Differenzenrechnung, Springer-Verlag, Berlin, 1924.
J50.315, 318

[6] Sur les valeurs asymptotiques des nombres et des polynômes de Bernoulli, C.R. Acad. Sci., Paris, 251 (1960), 2269-2270.
Z96,269; M23#A1078; R1962,5B44

[7] Sur les valeurs asymptotiques des nombres et des polynômes de Bernoulli, Rend. Circ. Mat. Palermo, 10 (1961), no. 1, 27-44.
Z96,269; M29#295; R1963,2B41

[8] De Bernoulli'ske Polynomier. Nyt Tidskr. Mat. B (1919), 33-41.

[9] De Euler'ske Polynomier. Nyt Tidskr. Mat. B (1919), 49-55.

[10] Sur les polynomes d'Euler. C. R. Acad. Sci., Paris, 169 (1919), 166-168.
J47.216

[11] Sur une extension des polynomes de Bernoulli. C. R. Acad. Sci., Paris, 169 (1919), 608-610.
J47.216

NORMI M.,
[1] On a convolution on the space of p-adic functions, Bull. Kyushu Inst. Tech. Math. Natur. Sci., 1989, no. 36, 11-20.
M90k:11159; R1990,2A328

NOVIKOV A.P.,
[1] The regularity of prime divisors of the first degree of an imaginary quadratic field. (Russian) Izv. Akad. Nauk. SSSR Ser. Mat., 33 (1969), 1059-1079.
Z188,352; M40#4239; R1970,3A387

NOWAK W.G.,
[1] On a problem of S. Chowla and H. Walum, Bull. Number Theory Related Topics, 7 (1982), no. 1, 1-10.
Z491.10013; 499.10012; M85e:11071; R1985,6A99

[2] An analogue to a conjecture of S. Chowla and H. Walum, J. Number Theory, 19 (1984), no. 2, 254-262.
Z546.10039; M85m:11056; R1985,6A100

NUNEMACHER J.,
[1] On computing Euler's constant, Math. Magazine, 65 (1992), no. 5, 313-322.
Z858.11067; M93j:65042

NUNEMACHER J., YOUNG R.M.,
[1] On the sum of consecutive kth powers, Math. Mag., 60 (1987), no. 4, 237-238.
Z625.10009; R1988,4V494


OBERHETTINGER F.: see also ERDÉLYI A., MAGNUS W., OBERHETTINGER F., TRICOMI F.

OBRESCHKOFF N.,
[1] Neue Quadraturformeln, Abhandl. der Preussisch. Akad. d. Wissen., math.-naturw. Kl., (1940), no. 4, 1-20.
J66.581; Z24,026; M2-284c

D'OCAGNE M.,
[1] Sur les nombres de Bernoulli, Bull. Soc. Math. France, 17 (1889), 107-109.
J21.248

[2] Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli. Bull. des sciences math. (2), 28 (1904), 29-32.
J35.449

ODLYZKO A.M., SCHÖNHAGE A.,
[1] Fast algorithms for multiple evaluation of the Riemann zeta function, Trans. Amer. Math. Soc., 309 (1988), no. 2, 797-809.
Z706.11047; M89j:11083; R1989,5G177

OESTERLÈ J.,
[1] Travaux de Ferrero et Washington sur le nombre de classes d'idéaux des corps cyclotomiques, Lect. Notes Math., 770 (1980), 170-182.
Z436.12003; M81i:12005; R1980,9A345

OETTINGER L.,
[1] Beiträge zur Summirung der Reihen, Archiv der Math. und Phys., 26 (1856), 1-42.

OHM M.,
[1] De nonnullis problematis analyticis caute tractandis, Mémoires présentés à l'Academie Imperiale des Sciences de St. Petersbourg par divers savants, 1 (1831), 109-130.

[2] Etwas über die Bernoulli'schen Zahlen, J. Reine Angew. Math., 20 (1840), 11-12.

OHTSUKI M.: see KATAYAMA K., OHTSUKI M.

OKADA S.,
[1] Generalized Maillet determinant, Nagoya Math. J., 94 (1984), 165-170.
Z535.12005; M85j:11147; R1985,12A387

[2] Kummer's theory for function fields, J. Number Theory, 38 (1991), no. 2, 212-215.
Z728.11031; M92e:11134

OKADA T.,
[1] Dirichlet series with periodic algebraic coefficients, J. London Math. Soc., 33 (1986), no. 1, 13-21.
Z589.10034; M87i:11087; R1986,12A114

OKAZAKI R.,
[1] On evaluation of $L$-functions over real quadratic fields. J. Math. Kyoto Univ., 31 (1991), no. 4, 1125-1153.
Z776.11071; M93b:11154

OLIVIER M.: see COHEN H., OLIVIER M.

OLSON F.R.,
[1] Some determinants involving Bernoulli and Euler numbers of higher order, Pacific J. Math., 5 (1955), 259-268.
Z68,284; M16-988i; R1956,3658

[2] Arithmetical properties of Bernoulli numbers of higher order, Duke Math. J., 22 (1955), 641-653.
Z66,281; M17-238b; R1956,5709

OLSON F.R.: see also CARLITZ L., OLSON F.R.

OLTRAMARE G.,
[1] Mémoire sur les nombres inférieurs et premiers, à un nombre donné, Mémoire de l'Inst. Nat. Genèvois, 4 (1856), 1-10.

OLVER F.W.J.,
[1] Asymptotics and special functions. Academic Press, New York, 1974. xvi + 572 pp.
Z303.41035; M55#8655; R1975,3B32K

ONG Y.L.: see EIE M., ONG Y.L.

ONO K.,
[1] Indivisibility of class numbers of real quadratic fields, Compositio Math. 119 (1999), no. 1, 1-11.

ONO K.: see also BALOG A., DARMON H., ONO K.

OPOLKA H.: see SCHARLAU W., OPOLKA H.

ORIAT B.,
[1] Lien algébrique entre les deux facteurs de la formule analytique du nombre de classes dans les corps abéliens, Acta Arith., 46 (1986), no. 4, 331-354.
Z615.12005; M88c:11063; R1987,6A370

ORIGUCHI T., KIRIYAMA H., MATSUOKA Y.,
[1] A table of the explicit formulas for the sums of powers $S_p(n) = \sum_{k=1}^n k^p$ for $p=1(1)61$. Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem., No. 20 (1987),1-31. Corrigenda: Ibid. 22 (1989), 133-134.
Z682.10011,697.10008; M89e:11016

[2] A table of the explicit formulas for the sums of powers $S_p(n) = \sum_{k=1}^n k^p$ for $p=1(1)61$. Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem., No. 21 (1988), 49-64.
Z682.10012; M90g:11026

ORTEGA ARAMBURU J.M.
[1] Euler, series y algunas funcciones especiales, Butl. Soc. Catalana Ciènc. Fís. Quím. Mat. (2), 2 (1984), no. 4, 384-404.
Z545.01004; M86i:01026

OSIPOV Yu.V.,
[1] p-adic Fourier transform. (Russian) Uspekhi. Mat. Nauk., 34 (1979), no. 5(209), 227-228.
Z431.43004; M81b:12021; R1980,4B987

[2] p-adic zeta-functions and Bernoulli numbers. (Russian) Studies in number theory, 6, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 93 (1980), 192-203, 228.
Z467.12019; M81f:12012; R1980,9A344

[3] On p-adic distributions. (Russian) Uspekhi Mat. Nauk., 37 (1982), no. 3(225), 193-194.
Z498.43007; M84d:12016; R1982,11B963

ÖSTLUND J.,
[1] Ett elementärt bevis för Bernoullis formel för potenssummor. Ark. för Mat., Astron. och Fys., 8 (1912), no. 12, 3p.
J(43.345)

[2] Sur le théorème de v. Staudt concernant le propriétés des nombres de Bernoulli. Ark. för Mat., Astron. och Fys., 11 (1916), 4 p.
J46.358

OSTMANN H.-H.,
[1] Additive Zahlentheorie, Teil II. Springer-Verlag, Berlin, 1956. 133 pp.
Z72,31; M20#5176; R1957,1137

OSTROGRADSKY M.V.,
[1] Mémoire sur les quadratures définies, Zap. Peterb. Akad. Nauk, VI ser., Fiz.-mat. Nauki, 2 (1841), 322-323.

OSTROWSKI A.,
[1] On the zeros of Bernoulli polynomials of even order, Enseign. Math. (2), 6 (1960), 27-47. (Collected Mathematical Papers, vol. 1, 764-784.)
Z103,254; M23#A3868; R1962,1B48

OTSUBO T.,
[1] Algebraic surfaces derived from quaternion algebras over real quadratic fields, Siatama Math. J., 3 (1985), 1-10.
Z607.14028; M87b:14018; R1986,5A541

OUTLAW C., SARAFYAN D., DERR L.,
[1] Generalization of the Euler-Maclaurin formula for Gauss, Lobatto and other quadrature formulas, Rend. Mat. (7), 2 (1982), no. 3, 523-530.
Z508.65008; M84i:65031; R1983,7B1015

OVERHOLTZER G.,
[1] A new application of the Schur derivative, Bull. Amer. Math. Soc., 51 (1945), no. 4, 313-324.
Z60,086; M6-255f

[2] Sum functions in elementary $p$-adic analysis, Amer. J. Math., 74 (1952), 332-346.
M14-21g

OWENS R.W.,
[1] Sums of powers of integers. Math. Mag., 65 (1992), no. 1, 38-40.
Z765.11007; M93a:11017

ÖZLÜK A.E., SNYDER C.,
[1] An identity involving Nörlund polynomials, Bull. Austral. Math. Soc., 43 (1991), no. 2, 307-315.
Z711.11011; M92c:11046; R1991,11B25


PAASCHE I.,
[1] 3 Arten von Linearverbindungen bei Bernoullipolynomen, Mat. Vesnik (N.S.), 9 (1972), 225-226.
Z249.05009; M48#114; R1973,5V41

LE PAIGE C.,
[1] Note sur les nombres de Bernoulli, C.R. Acad. Sci., Paris, 81 (1875), 966-967.
J7.132

[2] Relation nouvelle entre les nombres de Bernoulli, Bull. Acad. Royal Belgique, Cl. Sci. (2), 41 (1876), 1017.
J8.147

[3] Sur les nombres de Bernoulli et sur quelques fonctions qui s'y rattachent, Ann. Soc. Sci. Bruxelles, 1B (1876), 43-50.
J8.147

[4] Sur une formule de Scherk, Nouv. Corres. Math., 3 (1877), 159-161.

[5] Sur le développement de $\cot x$. Extrait d'une lettre adressée à M. Hermite. C.R. Acad. Sci., Paris, 88 (1879), 1075-1077.
J11.187

PAK I. M.: see KUZNETSOV A. G., PAK I. M., POSTNIKOV A. E.

PANCHISHKIN A.A.,
[1] Nearkhimedovy avtomorfnye dzeta-funktsii [Non-archimedean automorphic zeta functions]. Moskva: Izd. MGU, 1988, 140 pp.
Z667.10017; R1988,9A95K

[2] Non-archimedean L-functions associated with Hilbert modular forms. Max-Planck-Institut für Mathematik, Bonn, MPI/89-54, 59 pp.

[3] Non-archimedean L-functions associated with Siegel modular forms. Max-Planck-Institut für Mathematik, Bonn, MPI/89-55, 99 pp.

[4] Automorphic forms, $L$-functions, and $p$-adic analysis. Aleksandrov, I. A. (ed.) et al., Second Siberian winter school ``Algebra and Analysis''. Proceedings of the second Siberian school, Tomsk State University, Tomsk, Russia, 1989. Transl. ed. by Simeon Ivanov. Providence, RI: American Mathematical Society, Transl., Ser. 2, Am. Math. Soc. 151, 121-134 (1992).
Z871.11040

[5] Non-archimedean zeta functions associated with automorphic forms. In: International Conference, Automorphic functions and their applications. Khabarovsk, 27 June - 4 July 1988. Inst. Appl. Math., Acad. Sci. USSR, Khabarovsk, 1990, 135-162.
Z761.11025; M92f:11075

[6] Non-Archimedean $L$-functions of Siegel and Hilbert modular forms. Lecture Notes in Mathematics, 1471, Springer-Verlag, Berlin, 1991. vi+157pp.
Z732,*11026; M93a:11044

[7] Generalized Kummer congruences and $p$-adic families of motives. MSRI Preprint no. 030-95, Berkeley, CA, 1995.

[8] Non-archimedean Mellin transform and $p$-adic $L$-functions, Vietnam J. Math., 25 (1997), no.3, 179-202.
Z980.41357

PANCHISHKIN A.A.: see also MANIN YU.I., PANCHISHKIN A.A.

PANDAY P.: see KHANNA I.K., PANDAY P.

PÁNEK A.,
[1] Das System der Bernoullischen Zahlen, Prag, 1877.

PARASHAR B.P.,
[1] On generalized exponential Euler polynomials, Indian J. Pure Appl. Math., 15 (1984), no. 12, 1332-1339.
Z561.33004; M86f:05019; R1985,8B11

PARENT D.P.,
[1] Exercises in number theory. Springer-Verlag, New York, 1984. x + 541 pp.
Z536.10001; M86f:11002; R1985,5A102

PARODI M.,
[1] Fonction $\zeta$ de Riemann et nombres de Bernoulli, C.R. Acad. Sci., Paris, 240 (1955), 1395-1396.
Z64,69; M16-798d; R1956,129

[2] Matrices d'operateurs linéaires et polynômes orthogonaux. Application: polynômes de Bernoulli et polynômes de Tchebicheff, C. R. Acad. Sci. Paris A, 263 (1966), 279-281.
Z144,66; M34#1585; R1967,3B52

PARRY C.J.: see HAO F.H., PARRY C.J.

PARSON L., ROSEN K.,
[1] Hecke operators and Lambert series. Math. Scand., 49 (1981), no. 1, 5-14.
Z472.10017; M83d:10031

PASCAL E.,
[1] I determinanti ricorrenti e i nuovi numeri pseudo-Euleriani, Rend Ist Lomb., serie II, 40 (1907), 461-475.
J38.199

[2] I nuovi numeri pseudo-tangenziali, Rend. Palermo, 23 (1907), 358-366.
J38.466

[3] Repertorium der höheren Mathematik, Druck und Verlag von B. G. Teubner Leipzig, 1910.
J41.44,45

PATASHNIK O.: see GRAHAM R.L., KNUTH D.E., PATASHNIK O.

PATTERSON S.J.,
[1] An Introduction to the Theory of the Riemann Zeta-Function. Cambridge Univ. Press, Cambridge, 1988. xi + 156 pp.
Z641.10029; M89d:11072; R1988,9A96K

PEANO G.,
[1] Formulaire de Mathématique. Paris, 1901.
J32.69

PEDERZOLI G.: see MATHAI A.M., PEDERZOLI G.

PEDRO: see ALVARADO R., PEDRO

PENNEY D.E., POMERANCE C.,
[1] Multiplicative relations for sums of initial k-th powers, Amer. Math. Monthly, 92 (1985), no. 10, 729-731.
Z597.10011; M87d:11010; R1986,7A101

PENNY C.,
[1] Arts. Numbers of Bernoulli and Series, 1833. (Quoted from Ely [1]).

PEREIRA N.C.,
[1] Fermat's conjecture. (Portuguese). Bol. Soc. Port. Mat. No. 9 (1986), 18-22.
Z623.10001; M88a:11001

PEREMANS W.: see DUPARC H.J.A., PEREMANS W.

de PESLOUAN L.: see DE PESLOUAN L.

PETERMANN Y.-F.S.,
[1] Divisor problems and exponent pairs, Arch. Math., 50 (1988), 243-250.
Z619.10034; M89i:11104; R1988,10A126

[2] About a theorem of Pado Codeca's and $\Omega$-estimates for arithmetical convolutions: Addendum, J Number Theory, 36 (1990), no. 3, 322-327.
Z732.11048; M91j:11079

PETERSON H.,
[1] Modulfunktionen und quadratische Formen, Springer-Verlag, Berlin-New York, 1982. x + 307pp.
Z493.10033*; M85h:11021; R1983,5A386K

PETR K.,
[1] Poznamka k cislum Bernoulliho [A note on Bernoulli numbers], Casopis pest. mat. a fyz., 28 (1899), 24-27, (Czech).
J30.386

[2] On the Bernoulli polynomials, Rozpravy II. Trídy Ceské Akad., no. 40, 53 (1943), 16pp., (Czech).
Z63/II; M9-411a

[3] Über die Bernoullischen Polynome, Acad. Tchèque Sci. Bull. Int. Cl. Sci. Math. Nat., 44 (1943), 511-526. (German translation of [2]).
M8-441a

PETRENKO A.K., PETRENKO O.L.,
[1] The Babbage machine and the origin of programming. (Russian). Istor.-Mat. Issled. No. 24 (1979), 340-360, 389.
Z446.01017; M83b:01045; R1979,11A24

PETROVA S. S.,
[1] Euler-Maclaurin's summation formula and asymptotic series. (Russian) Istor. Metodol. Estestv. Nauk., no. 36 (1989), 103-108.
Z715.01011; M92f:01021

PETROVA S.S., SOLOVJEV A.A.,
[1] The calculus of variations. Theory of finite differences. (Russian). "Nauka", Moscow, 1987, 307 pp.
Z629.01011; M90a:01040

PFEIFFER G.V.,
[1] Zametka o funktsiyakh Bernulli [A note on Bernoulli functions]. Izvestiya. Kievsk. Universiteta, No. 11, (1905), 115-119.
J36.449

PFISTER F.,
[1] Bernoulli numbers and rotational kinematics, Trans. ASME J. Appl. Mech. 65 (1998), no. 3, 758-763.
M99i:70004

PHATAK M.S.,
[1] Sums of powers of natural numbers. Indian J. Pure Appl. Math., 21 (1990), no. 10, 879-887.
Z715.11013; M91i:11021; R1991,6V511

PHILLIPS E.G.,
[1] Note on summation of series J. London Math. Soc., 4 (1929), 114-116.
J55.I.131

PIERCE T. A.,
[1] Note on Bernoulli's numbers. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 199.
J(48.255)

PIETROCALA C.,
[1] Sui numeri e polinomi di Bernoulli, Giorn. mat., Napoli, 34 (1896), 48-72.
J27.212

PINK R.: see HARDER G., PINK R.

PINTÉR Á.,
[1] A note on the equation $1\sp k+2\sp k+\cdots+(x-1)\sp k=y\sp m$, Indag. Math., New Ser. 8 (1997), no. 1, 119-123.
Z876.11014

PINTÉR Á.: see BRINDZA B., PINTÉR Á.

PIOUI R.,
[1] Module de continuité des fonctions $L$ $2$-adiques des charactères quadratiques. Manuscr. Math., 75 (1992), no. 2, 167-195.
Z763.11044; M93f:11092; R1994,2A327

PLANA G.A.A.,
[1] Note sur une nouvelle expression analytique des nombres Bernoulliens, propre à exprimer en termes finis la forme générale pour la sommation des suites, Mém. Acad. Sci., Turin (1), 25 (1820), 403-418.

PLATONOV M.L.,
[1] Combinatorial numbers of a class of mappings and their applications. (Russian). Moscow: Nauka, 1979, 151 pp.
Z597.05004; M83m:05018; R1980,2V593K

[2] Combinatorial numbers. (Russian). Irkutsk: Irkutsk Univ. Publ., 1980, 104 pp.

PLOUFFE S.: see SLOANE N.J.A., PLOUFFE S.

POGREBISSKII I.B., STOKALO I.Z.,
[1] Zhizn' i nauchnaya deyatel'nost' G.F. Voronogo [Life and scientific activity of G. F. Voronoi]. In: Voronoi, G.F., Sobranie sochinenii v trekh tomakh. (Russian) [Collected works in three volumes.] Vol. III, Kiev, 1953, 263-304.
Z49,28; M16-2d; R1954,3228K

POISSON S.D.,
[1] Mémoire sur le calcul numérique des intégrales définies, Mém. Acad. Sci. Inst. de France, 6 (1823), 571-602.

POITOU G.: see COATES J., POITOU G.

POLI L.,
[1] Tangentes d'ordre supérieur et nombres de Bernoulli généralisés. Ann. Univ. Lyon Sect. A (3), 12 (1949), 5-25.
M12-96f

POLLACZEK F.,
[1] Über den grossen Fermatschen Satz, Sitzungsb. Kais. Akad. Wiss., Wien, Math.-Natur. Kl., Abteil. 2a, 126 (1917), 45-59.
J46.193

[2] Über die irregulären Kreiskörper der $l$-ten und $l^2$-ten Einheitswurzeln, Math. Zeit., 21 (1924), 1-38.
J50.111

[3] Relations entre les dérivées logarithmiques de Kummer et les logarithmes $\pi$-adiques, Bull. Sci. Math., (2), 70 (1946), 199-218.
Z63,734; M9-273d

POLOVINKIN V. I.,
[1] Approximations of the Bernoulli polynomials by constants and applications tothe theory of quadrature formulas, Siberian Adv. Math., 8 (1998), no. 2, 110-121.
Z915.41020; M99j:41046

POLYA G., SZEGÖ G.,
[1] Aufgaben und Lehrsätze aus der Analysis, Berlin, 1925, 2te Aufl., Berlin, Springer-Verlag, Bd. 1, 1954, xvi + 338S.; Bd. 2, 1954, x+407S.
Z55,278; M15-512a,b; R1956,5294K

[2] Problems and theorems in analysis. 2 Vols., Springer-Verlag, New York-Berlin, 1972, 1976.
M49 #8782, 53 #2

POMERANCE C.: see PENNEY D.E., POMERANCE C.

POMERANCE C.: see also CRANDALL R.E., DILCHER K., POMERANCE C.

van der POORTEN A.,
[1] Notes on Fermat's last theorem. Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons, Inc., New York, 1996. xviii+222 pp.
Z882.11001; M98c:11026

POPOV B. S.,
[1] Expressions of Laguerre polynomials through Bernoulli polynomials. Mat. Bilten No. 22, (1998), 15-18.
M2000e:33011

PORUBSKÝ S.,
[1] Covering systems and generating functions, Acta Arith., 26 (1975), no. 3, 222-231.
Z(268.10044),306.10003; M52#328; R1976,2A158

[2] A characterization of finite unions of arithmetic sequences, Discrete Math., 38 (1982), no. 1, 73-77.
Z473.05001; M84a:10057; R1982,7V481

[3] Further congruences involving Bernoulli numbers, J. Number Theory, 16 (1983), no. 1, 87-94.
Z507.10008; M85b:11015; R1983,9A76

[4] Voronoi's congruence via Bernoulli distribution, Czechoslovak Math. J., 34 (109) (1984), no. 1, 1-5.
Z543.10012; M85g:11024; R1984,9A92

[5] Identities involving covering systems, I. Math. Slovaca, 44 (1994), no. 2, 153-162.
Z821.11008; M95f:11002; R1995,2A63

[6] Identities involving covering systems, II, Math. Slovaca, 44 (1994), no. 5, 555-568.
Z821.11008; M96e:11006; R1997,2A35

[7] Voronoi Type Congruences for Bernoulli Numbers, in: "Voronoi's Impact on Modern Science" (P. Engel and H. Syta, eds.), Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, 1998.

POSTNIKOV A. E.: see KUZNETSOV A. G., PAK I. M., POSTNIKOV A. E.

POSTNIKOV M.M.,
[1] Fermat's theorem. (Russian) Moscow, 1978, 128 pp.
M58#21906

[2] Introduction to algebraic number theory. (Russian) "Nauka", Moscow, 1982, 240 pp.
Z527.12001*; M85d:11001; R1982,10A99K

POUSSIN F.,
[1] Sur une propriété arithmétique de certains polynômes associés aux nombres d'Euler, C.R. Acad. Sci. Paris Sér. A-B, 266 (1968), A392-A393.
Z155,27; M39#1338; R1968,9A140

POUSSIN F.-H.,
[1] Polynômes et nombres d'Euler. Thèse de doctorat de 3e cycle, Paris, 1970.

PRABHAKAR T.R., GUPTA S.,
[1] Bernoulli polynomials of the second kind and general order, Indian J. Pure Appl. Math., 11 (1980), no. 10, 1361-1368.
Z483.33007; M81m:05011; R1981,4V378

PRABHAKAR T.R., REVA,
[1] An Appel cross-sequence suggested by the Bernoulli and Euler polynomials of general order, Indian J. Pure Appl. Math., 10 (1979), no. 10, 1216-1227.
Z414.33008; M81c:10018; R1981,4V374

[2] An Appel sequence general nature, Math. Stud., 50 (1982), no. 1-4, 116-123 (1987).
Z708.33008; M90e:33033; R1989,8B20

PRABHU S.,
[1] Some integrals involving Euler and Bernoulli numbers, J. Indian Inst. Sci., 50 (1968), no. 3, 238-243.
M38#1292; R1969,6B19

PRASAD J.: see AGRAWAL B.D., PRASAD J.

PRASAD S.: see SINGH R., PRASAD S.

PREECE C.T.,
[1] Theorems stated by Ramanujan (III): Theorems on transformation of series and integrals, J. London Math. Soc., 3 (1928), 274-282.
J54.250

DE PRESLE A.G.V.,
[1] Determination des nombres de Bernoulli, Bull. Soc. Math. France, 14 (1886), 100-103.
J18.288

PRESTEL A.: see EBBINGHAUS H.-D. et al.

PRODINGER H.,
[1] How to select a loser, Discrete Math., 120 (1993), no. 1-3, 149-159.
Z795.90103; M94g:05010

PRODINGER H.: see also FLAJOLET P., PRODINGER H.

PROPAVESSI D. T.,
[1] On Jacobi sum Hecke characters ramified only at 2. J. Number Theory, 38 (1991), 161-184.
M92k:11122

PROUHET M.E.,
[1] Note sur la solution précédente, Nouv. Ann. de Math. (Paris), 10 (1851), 328-330.

PUPPO G.,
[1] Sulle somme delle potenze simili dei numeri interi, e sui numeri di Bernoulli et di Stirling, Atti Instituto Veneto, 91 (1932), no. 2, 925-932.
J58.I.160

PUTNAM T. M.,
[1] Residues of certain sums of powers of integers. Amer. Math. Monthly, 21 (1914), no. 7, 220-221.
J45.II.332

QUEEN C.,
[1] A note on class numbers of imaginary quadratic fields, Arch. Math., 27 (1976), no. 3, 295-298.
Z334.12008; M53#10760; R1976,12A165

[2] The existence of p-adic Abelian L-functions. Number theory and algebra, pp. 263-280. Academic Press, New York, 1977.
Z371.12015; M58#5598


RAAB W.,
[1] Teilbarkeitseigenschaften verallgemeinerter Tangentialkoeffizienten, J. Reine Angew. Math., 241 (1970), 7-14.
Z192,390; M41#3409; R1970,7A122

RAABE J.L.,
[1] Die Differential- und Integralrechnung mit Funktionen einer Variablen, Zürich, 1839, Bd. 1.

[2] Angenäherte Bestimmung der Factorenfolge $1 \cdot 2 \cdots n = \Gamma (1+n) = \int x^n e^{-x}dx$, wenn n eine sehr grosse Zahl ist, J. Reine Angew. Math., 25 (1843), 146-159.

[3] Angenäherte Bestimmung der Function \Gamma (1+n) = \int_0^{\infty} x^n e^{-x}dx$, wenn $n$ eine ganze, gebrochene, oder incommensurable sehr grosse positive Zahl ist, J. Reine Angew. Math., 28 (1844), 10-18.

[4] Die Jacob Bernoullische Funktion, Zürich, 1848.

[5] Zurückführung einiger Summen und bestimmter Integrale auf die Jacob Bernoulli'sche Funktion, J. Reine Angew. Math., 42 (1851), 348-367.

[6] Mathematische Mittheilungen (2 volumes), Zürich, Verlag von Meyer & Zeller, 1857, 1858.

RADEMACHER H.,
[1] Topics in analytic number theory, Springer-Verlag, Berlin, 1973.
Z253.10002*; M51#358; R1973,11A116K

RADEMACHER H., GROSSWALD E.,
[1] Dedekind sums. The Math. Assoc. of America, Washington, D.C., 1972. xvi + 102 pp.
Z251.10020; M50#9767; R1973,11A116K

RADICKE A.,
[1] Solutions des questions proposées, Nouv. Corres. Math., 5 (1879), 33; 6 (1880),69-72.

[2] Extrait d'une lettre, Nouv. Corres. Math., 5 (1879), 196.

[3] Démonstration d'un théorème de Stern, Nouv. Corres. Math., 6 (1880), 507-509.
J12.194

[4] Die Recursions-formeln für die Berechung der Bernoullischen und Eulerschen Zahlen, Louis Nebert, Halle a.S., 1880, 35 pp.
J12.193

[5] Démonstration du théorème de Staudt et de Clausen, Nouv. Corres. Math., 6 (1880), 503-507.
J12.194

[6] Zur Theorie der Eulerschen Zahlen, J. Reine Angew. Math., 89 (1880), 257-261.
J12.193

RADO R.,
[1] A new proof of a theorem of v. Staudt, J. London Math. Soc., 9 (1934), 85-88.
J60.I.115; Z14,011

[2] A note on the Bernoullian numbers, J. London Math. Soc., 9 (1934), 88-90.
J60.I.115; Z9,150

RAI B.K., RAI N., SINGH S.N.,
[1] On generalized Bernoulli and Euler polynomials, Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.), 25(73) (1981), no. 3, 307-311.
Z475.33009; M83e:33008; R1982,7B29

RAI B.K., SINGH S.N.,
[1] On the extension of Bernoulli and Euler polynomials, Proc. Nat. Acad. Sci. India A, 52 (1982), no. 2, 207-216.
Z514.05006; M85a:33018; R1984,2B43

[2] Properties of some extended Bernoulli and Euler polynomials, Fibonacci Quart., 21 (1983), no. 3, 162-173.
Z529.10016; M85f:05005

RAI B.K.: see also SINGH S.N. et al.

RAI N.: see RAI B.K., RAI N., SINGH S.N.

RAI V.S., SINGH S.N.,
[1] Certain properties of extended Euler and Bernoulli polynomials, Tamkang J. Math., 16 (1985), no. 4, 1-12.
Z598.10025; M87f:11016; R1987,3A133

[2] A two-variable generalization of Bernoulli and Euler polunomials (Hindi). Vijnana Parishad Anusandhan Patrika, 29 (1986), no. 1, 27-34.
M88j:33013

[3] On extended Bernoulli and Euler polynomials, Proc. Nat. Acad. Sci. India, A 57 (1987), no. 4, 411-426.
Z673.10009; M90h:05016; R1989,3B22

RAI V.S.: see also SINGH S.N., RAI B.K., RAI V.S.

RAMACHANDRA K., SANKARANARAYANAN A.,
[1] A remark on ${\zeta}(2n)$, Indian J. Pure Appl. Math., 18 (1987), no.10, 891-895.
Z635.10036; M89a:11087; R1988,6A108

RAMAKRISHNAN D.,
[1] Regulators, algebraic cycles and values of $L$-functions. Algebraic $K$-theory and algebraic number theory, Proc. Semin., Honolulu/Hawaii 1987, Contemp. Math., 83 (1989), 183-310.
Z694.14002; M90e:11094

RAMANUJAN S.,
[1] Some properties of Bernoulli's numbers, J. Indian Math. Soc., 3 (1911), 219-234.
J42.460

[2] Collected Papers, Cambridge Univ. Press, Cambridge, 1927, xxxvi + 355 pp.; reprinted: Chelsea Publ., New York, 1962.
J53.30

[3] Notebooks vol. 1, 2, Tata Inst. Fundamental Research, Bombay, 1957.
M20#6340

RANDRIANARIVONY A.,
[1] Fractions continues, $q$-nombres de Catalan et $q$-polynomes de Genocchi. (French) [Continued fractions, $q$-Catalan numbers and $q$-Genocchi polynomials] European J. Combin. 18 (1997), no. 1, 75-92.
Z872.05001; M98e:05007

RANDRIANARIVONY A., ZENG JIANG,
[1] Sur une extension des nombres d'Euler et les records des permutations alternantes. Séminaire Lotharingien de Combinatoire (Gerolfingen, 1993), 97-110, Prépubl. Inst. Rech. Math. Av., 1993/34, Univ. Louis Pasteur, Strasbourg, 1993.
M95j:05023

[2] Sur une extension des nombres d'Euler et les records des permutations alternantes, J. Combin. Theory A, 68 (1994), no. 1, 86-99.
Z809.05002; M95k:05011

[3] Une famille de polynômes qui interpole plusieurs suites classiques de nombres. Séminaire Lotharingien de Combinatoire (Saint Nabor, 1993), 103-126, Prépubl. Inst. Rech. Math. Av., 1994/21, Univ. Louis Pasteur, Strasbourg, 1994.
M95m:11020

[4] Une famille de polynomes qui interpole plusieurs suites classiques de nombres. Adv. in Appl. Math. 17 (1996), no. 1, 1-26.
Z874.05005; M97e:05009

[5] Some equidistributed statistics on Genocchi permutations. The Foata Festschrift. Electron. J. Combin. 3 (1996), no. 2, Research Paper 22, approx. 11 pp. (electronic).
Z857.05002; M97k:05012

RANDRIANARIVONY A.: see also DUMONT D., RANDRIANARIVONY A.

RANDRIANARIVONY A.: see also HAN G.-N.; RANDRIANARIVONY A.; ZENG J.

RANKIN R.A.,
[1] Modular forms and functions. Cambridge Univ. Press, Cambridge-New York-Melbourne, 1977. xiii + 384 pp.
Z376.10020; M58#16518; R1979,1A509

[2] On certain meromorphic modular forms, Analytic number theory, Vol. 2 (Allerton Park, IL, 1995), 713-721, Progr. Math., 139, Birkhäuser Boston, Boston, MA, 1996.
Z862.11032; M97f:11034

RASSIAS T.M.: see HARUKI H., RASSIAS T.M.

RATCLIFFE J.G., TSCHANTZ S.T.,<\a>
[1] Volumes of integral congruence hyperbolic manifolds, J. Reine Angew. Math. 488 (1997), 55-78.
Z873.11031; M99b:11076

RAY G.A.,
[1] Relations between Mahler's measure and values of L-series, Canad. J. Math., 39 (1987), no. 3, 694-732.
Z621.12005; M88m:11071; R1988,4A87

RAY N.,
[1] Extensions of umbral calculus I: Penumbral coalgebras and generalized Bernoulli numbers, Adv. Math., 61 (1986), no. 1, 49-100.
Z631.05002; M88b:05019; R1987,3A422

[2] Stirling and Bernoulli numbers for complex oriented homology theory. In: G. Carlsson et al. (Eds.), Algebraic Topology (Arcata, CA, 1986), 362-373, Lecture Notes in Math., 1370, Springer-Verlag, Berlin-New York, 1989.
Z698.55002; M90f:55010; R1990,5A525

RAY N.: see BAKER A.J. et al.

RAZAR M.J.: see GOLDSTEIN L.J., RAZAR M.J.

RECKNAGEL W.,
[1] Über eine Vermutung von S. Chowla and H. Walum, Arch. Math., 44 (1985), no.4, 348-354.
Z556.10032; M86i:11051; R1985,10A126

[2] Über eine zum Kreisproblem verwandte Summe, Monatsh. Math., 100 (1985), no. 4, 293-298.
Z568.10024; M87b:11083; R1986,5A138

[3] Über eine Verallgemeinerung des Problems von Chowla und Walum, Arch. Math., 46 (1986), no. 2, 148-152.
Z588.10050; 551.10008; M87g:11114; R1986,9A84

[4] Über ein Analogon zu einem Satz von Walfisz, Comm. Math. Univ. St. Paul., 36 (1987), no. 1, 13-20.
Z629.10033; M88f:11099; R1988,9A133

REDFERN E.J.: see ALLENBY R.B.J.T., REDFERN E.J.

REICHERT M.A.,
[1] Détermination explicite des courbes elliptiques ayant un groupe de torsion non trivial sur des corps de nombres quadratiques sur Q. Séminaire de théorie des nombres, Univ. Bordeaux I, année 1983-84, exp. no. 11, 33 pp.
Z562.14009; M86h:11049

REMMERT R.: see EBBINGHAUS H.-D. et al.

REMOROV P.N.,
[1] On Kummer's theorem. (Russian) Leningrad. Gos. Univ. Uch. Zap. Ser. Mat. Nauk., 144(23) (1952), 26-34.
M18-381b

[2] Ob otsenke chisla klassov krugovogo polya [On an estimation of the class number of a cyclotomic field]. XXVII Gertsenovsk. chteniya, Matematika, Nauchn. Dokl., Leningrad, 1974, 19-22.
R1974,10A165

RENFER H.,
[1] Die Definitionen der Bernoullischen Funktion und Untersuchung zur Frage, welche von denselben für die Theorie die zutreffendste ist. Inaugural Dissertation, Bern, 1900, 100pp.
J31.437

REVA: see PRABHAKAR T.R., REVA

REY PASTOR J.,
[1] Polinomios correlativos de los de Bernoulli. Boletín Seminario mat. Argentino, 1 (1929), 1-10.
J55.II.798

RIBENBOIM P.,
[1] Recent results on Fermat's Last Theorem, Canad. Math. Bull., 20 (1977), no. 2, 229-242.
Z355.10015; M57#3050; R1978,5A132

[2] Some criteria for the first case of Fermat's last theorem, Tokyo J. Math., 1 (1978), 149-155.
Z381.10012; M58#10723; R1979,2A132

[3] Fermat's last theorem: recent developments. Sémin. Théor. Nombres, 1978-79, Exp. No. 17, 22 pp., CNRS, Talence, 1979.
Z418.10022; M81m:10025

[4] 13 Lectures on Fermat's Last Theorem, Springer-Verlag, New York- Heidelberg-Berlin, 1979.
Z456.10006*; M81f:10023; R1980,8A113K

[5] Fermat's last theorem: Recent developments. Jahrbuch Überblicke Math., 1980, pp. 75-92. Bibliographisches Institut, Mannheim, 1980.
Z458.10016; M82h:10023

[6] The work of Kummer on Fermat's last theorem. Number theory related to Fermat's last theorem (Cambridge Mass., 1981), 1-29, Progr. Math., 26, Birkhäuser, Boston, Mass., 1982.
Z498.12002; M85d:11028; R1985,2A356

[7] Kummer's ideas on Fermat's last theorem, Enseign. Math., 29 (1983), 165-177.
Z521.12002; M85c:01029; R1983,11A6

[8] "1093", Math. Intelligencer, 5 (1983), no. 2, 28-34.
Z516.10001; M85e:11001; R1983,12A100

[9] Krasner versus Fermat, Queen's Mathematical Preprint No. 1983-11 (Kingston, Ont., Canada), 8 pp.

[10] Il mondo Krasneriano, Queen's Mathematical Preprint No. 1983-12 (Kingston, Ont., Canada), 158 pp.

[11] A história do último teorema de Fermat (Portuguese)(The history of Fermat's last theorem), Bol. Soc. Paran. Mat. (2), 5 (1984), no. 1, 14-32.
Z545.10002; M85m:01009; R1985,7A16

[12] Impuissants devant les puissances, Exposition. Math. 6 (1988), no. 1, 3-28.
Z635.10013; M89c:11045

[13] Prime number records (a new chapter for the Guinness Book of Records).(Russian), Uspekhi Mat. Nauk, 42 (1987), no. 5 (257), 119-176.
Z642,10002; M89c:11181; R1988,2A105

[14] The book of prime number records. Springer-Verlag, New York-Berlin, 1988. xxiv + 476 pp.
Z642.10001; M89e:11052; R1989,4A50

[15] The Little Book of Big Primes. Springer-Verlag, New York etc., 1991, xvii+237pp.
Z734.11001; M92i:11008; R1991,8A159

[16] Prime number records. (Spanish) Translated from the English by V. S. Albis Gonzalez. Lect. Mat. 12 (1991), no. 1-3, 137-158.
Z817.11003; M94j:11008

[17] Prime number records. Nieuw Arch. Wisk. (4), 12 (1994), no. 1-2, 53-65.

[18] The new book of prime number records. Springer-Verlag, New York, 1996. xxiv+541 pp.
Z856.11001; M96k:11112

RIBET K.A.,
[1] A modular construction of unramified p-extensions of $Q(\mu_p)$, Inventiones Math., 34 (1976), no. 3, 151-162.
Z338.12003; M54#7424; R1977,6A253

[2] p-adic L-functions attached to characters of p-power order, Sémin. Delange-Pisot-Poitou, Théorie des Nombres, 19e année, 1977/1978, Exp. no. 9, 8pp.
Z394.12007; M80b:12012; R1979,7A393

[3] Fonctions L p-adiques et théorie d'Iwasawa (Notes by Ph. Satgé), Publ. Math. d'Orsay, Univ. Paris-Sud, Départ. Math., 1979.
Z445.12007; M81c:12022

[4] Report on p-adic L-functions over totally real field, Journées Arithmétiques de Luminy, Astérisque, Soc. Math. France, Paris, 61 (1979), 177-192.
Z408.12016; M81f:12009; R1979,10A233

[5] Sur la recherche des p-extensions non ramifiées de $Q(\mu_p)$, Groupe étude algèbre, Univ. P. et M. Curie, (1975-76), 1 (1978), no. 2, 1-3.
Z375.12007; M80f:12005; R1978,11A406

RIBET K.A.: see also DELIGNE P., RIBET K.A.

RICCI G.,
[1] Un perfezionamento dei teoremi di Sylvester, N. Nielsen, Saalschütz, Lipschitz sui numeri di Bernoulli, Giorn. di Mat. Battaglini, 69 (1931), 1-4.
J57.179; Z2,178

[2] Sui coefficienti binomiali e polinomiali. Una dimonstrazione del teorema di Staudt-Clausen sui numeri di Bernoulli, Giorn di Mat. Battaglini, 69 (1931) 9-12.
J57.180; Z2,179

RICCI P.E.: see DI CAVE A., RICCI P.E.

RIEGER G.I.,
[1] Eine Bemerkung über die Hurwitzschen Zahlen, J. Reine Angew. Math., 296 (1977), 212-216.
Z375.12007; M56#15550; R1978,8A112

TE RIELE H.J.J.: see IVIC A., TE RIELE H.J.J.

TE RIELE H.J.J.: see MOREE P., TE RIELE H.J.J., URBANOWICZ J.

RIESEL H.,
[1] Om rekursionsformuler för Bernoullis Tal, Nordisk Matem. Tidskrift, 9 (1961), 44-48, 95-96.
Z116,267; M23#A3101; R1962,6A106

[2] Bernoullis tal och von Staudts teorem, Elementa, 51 (1968), no. 3, 201-206.
R1969,4A69

[3] Some series related to infinite series given by Ramanujan, Nordisk. Tidsk. Informationsbehandling (BIT), 13 (1973), 97-113.
Z252.10040; M50#820; R1973,9B27

[4] A consequence of the von Staudt - Clausen theorem, Nordisk. Tidskr. Informationsbehandling (BIT), 14 (1974), 120-121.
Z271.10004; M49#199; R1974,8A113

[5] An "exact" formula for the $2n$-th Bernoulli number, Acta Arith., 26 (1975), 273-277.
Z271.10009; M51#10214; R1976,2A159

RIMSKII-KORSAKOV B.S.,
[1] Zametka ob obobshchennykh teoremakh umnozheniya bernullievykh polinomov i kinkelinovykh funktsij [A note on the generalized multiplication theorems for Bernoulli polynomials and Kinkelin functions]. Trudy. Moskovsk. aviatsionnogo instituta, 1947, no. 6, 49-52.

RIORDAN J.,
[1] Inverse relations and combinatorial identities, Amer. Math. Monthly 71 1964, 485-498.
Z; M30 #34; R1965,3A137

[2] Combinatorial identities. John Wiley & Sons, Inc., New York- London-Sidney, 1968. xiii $+$256pp. Reprint Robert E. Krieger Publ. Co., Huntington, N.Y., 1979.
Z194,5; M38#53; R1970,3V264K

RIORDAN J., STEIN P.R.,
[1] Proof of a conjecture on Genocchi numbers, Discrete Math., 5 (1973), no. 4, 381-388.
Z271.05004; M47#4919; R1974,1V304

RIORDAN J.: see also CARLITZ L., RIORDAN J.

RITTER J., WEISS A.,
[1] Cohomology of units and $L$-values at zero, J. Amer. Math. Soc. 10 (1997), no. 3, 513-552.
Z885.11059; M98a:11150

ROBBINS N.,
[1] Revisiting an old favourite: $\zeta(2m)$, Math. Mag. 72 (1999), no. 4, 317-319.

ROBERT A.M.,
[1] A note on the numerators of the Bernoulli numbers. Exposition. Math., 9 (1991), no. 2, 189-191.
Z738.11024; M92c:11017; R1991,12A67

ROBERT G.,
[1] Nombres de Hurwitz et régularité des idéaux premiers. Séminaire Delange - Pisot - Poitou (16e année: 1974/75), Fasc. 1, Exp. No. 21, 7 pp., Paris, 1975.
Z372.12011; M53#348; R1976,7A447

[2] Nombres de Hurwitz et unités elliptiques, Ann. Sci. École Norm. Sup. (4), 11 (1978), no. 3, 297-389.
Z409.12008; M80k:12010; R1979,8A360

RODRIGUEZ D.M.: see DEEBA E.Y., RODRIGUEZ D.M.

RODRIGUEZ VILLEGAS F.,
[1] The congruences of Clausen - von Staudt and Kummer for half-integral weight Eisenstein series. Math. Nachr., 162 (1993), 187-191.
Z805.11042; M94h:11048

RÖDSETH Ö. J.,
[1] A note on Brown and Shiue's paper on a remark related to the Frobenius problem, Fibonacci Quart., 32 (1994), no.5, 407-408.
Z840.11009; M95j:11022; R1997,11A154

ROGEL F.,
[1] Über den Zusammenhang der Facultäten-Coefficienten mit den Bernoullischen und Eulerschen Zahlen, Arch. Math. und Phys. (2), 10 (1891), 318-332.
J23.272

[2] Arithmetische Entwicklungen, Arch. Math. und Phys. (2), 11 (1892), 77-82.
J24.185

[3] Ein neues Recursionsgesetz der Bernoullischen Zahlen, Sitzungsb. Kgl. Böhmische Gesells. Wiss., Prag, (1895), No. 26, 1-4.
J26.286

[4] Die Entwicklung nach Bernoullischen Funktionen, Sitzungsb. Kgl. Böhmische Gesells. Wiss., Prag, (1896), No. 31, 1-48.
J27.329

[5] Die Entwicklung nach Bernoullischen Funktionen, Arch. Math. und Phys. (2), 17 (1899), 129-146.
J30.251

[6] Question 13781, Math. questions and solutions from "Educational Times", London, 70 (1899), 37-38.
J30.250

[7] Question 13868, Math. questions and solutions from "Educational Times", London, 70 (1899), 121-122.
J30.250

[8] Question 14066, Math. questions and solutions from "Educational Times", London, 71 (1899), 34-35.
J30.250

[9] Question 13959, Math. questions and solutions from "Educational Times", London, 71 (1899), 126-128.
J30.251

[10] Question 14194, Math. questions and solutions from "Educational Times", London, 72 (1900), 125-126.
J31.287

[11] Über Bernoullische und Eulersche Zahlen, Sitzungsber. d. kgl. Böhmischen Gesells. Wiss., Prag, (1907), No. 23, 1-27.
J38.316

[12] Theorie der Euler'schen Functionen. Sitzungsber. d. kgl. Böhm. Ges. Wiss., (1896), no. 2, 45p.
J27.333

[13] Note zur Entwicklung nach Euler'schen Funktionen. Sitzungsber. d. kgl. Böhm. Ges. Wiss., Prag., (1896), no. 42, 1-9.
J27.329

[14] Transformationen der harmonischen Reihen $S_{2n+1}$ und $U_{2n}$. Sitzungsber. d. kgl. Böhm. Ges. Wiss., Prag., (1907), no. 17, 14p.
J38.316

ROMAN S.,
[1] The umbral calculus, New York, Acad. Press Inc., (Pure and Appl. Math., 111 ) 1984.
Z536.33001; M87c:05015

ROMANOV N.P.,
[1] On an orthogonal system., Doklady Akad. Nauk SSSR (N.S.), 40 (1943), 257-258.
M6-49a

[2] On Hilbert space and the theory of numbers, II. (Russian) Izv. Akad. Nauk. SSSR. Ser. Mat., 15 (1951), 131-152.
Z44,40; M13-208g

[3] Ob odnom novom analiticheskom predstavlenii dzeta-funktsii Rimana [On a new analytical representation of the Riemann zeta function]. Trudy Sredneaz. Univ., (1956), vyp. 66, kn. 13, 51-54.
R1957,56

ROSE H.E.,
[1] A course in number theory. The Clarendon Press, Oxford University Press, New York, 1988. xii + 354 pp.
Z637.10002; M89f:11002

ROSELLE D.P.: see DILLON J.F., ROSELLE D.P.

ROSEN K.H., SNYDER W.M.,
[1] A Kummer congruence for the Hurwitz-Herglotz Function, Tokyo J. Math., 6 (1983), no. 1, 125-138.
Z561.10005; M84m:10018; R1984,2A432

[2] p-adic Dedekind sums, J. Reine Angew. Math., 361 (1985), 23-26.
Z561.10005; M87b:11037; R1986,4A396

ROSEN M.,
[1] Remarks on the history of Fermat's Last Theorem 1844 to 1984. Cornell, Gary (ed.) et al., Modular forms and Fermat's last theorem. Papers from a conference, Boston, MA, USA, August 9-18, 1995. New York, NY: Springer, 505-525 (1997).
Z893.11011

ROSEN M.: see also IRELAND K., ROSEN M.

ROSENHEAD L.: see FLETCHER A. et al.

ROSSI F.S., TOSCANO L.,
[1] Sui polinomi e sui numeri di Bernoulli e di Eulero, Archimede, 20 (1968), no. 3, 155-160.
Z165,361; M38#2354; R1969,2V204

ROTA G.-C.,
[1] Combinatorial snapshots, Math. Intelligencer 21 (1999), no. 2, 8-14.

ROTA G.-C., TAYLOR B.D.,
[1] An introduction to the umbral calculus. Analysis, geometry and groups: a Riemann legacy volume, 513-525, Hadronic Press, Palm Harbor, FL, 1993.
M96a:05015

[2] The classical umbral calculus, SIAM J. Math. Anal., 25 (1994), no. 2, 694-711.
Z797.05006; M95d:05014

ROTA G.-C.: see also DI CRESCENZO, ROTA G.-C.

ROTHE H.A.,
[1] Bekanntmachung für Mathematiker, Allgemeine Literatur-Zeitung, Halle, Bd. 1, No. 63 (1817), 503-504.

ROUGH M.,
[1] Some numbers related to the Bernoulli numbers, Math. Mag., 29 (1955), 101-103.
R1956,6352

ROVINSKY M.,
[1] Multiple gamma functions and $L$-functions. Math. Res. Lett. 3 (1996), no. 5, 703--721.
Z867.11061; M98b:11093

ROY Y.: see CARTIER P., ROY Y.

RUBIN K.,
[1] Congruences for special values of L-functions of elliptic curves with complex multiplication, Invent. Math., 71 (1983), no. 2 339-364.
Z513.14012; M84h:12018; R1983,7A409

[2] The main conjecture. Appendix to: Cyclotomic Fields by S. Lang, 2nd ed., Springer-Verlag, New York, 1990.
M91c:11001

[3] Kolyvagin's system of Gauss sums. Proc. Conf., Texel/Neth. 1989, Prog. Math., 89 (1991), 309-324.

RUBIN K.: see also LANG S. [7]

RUBIN K., WILES A.,
[1] A Mordell-Weil group of elliptic curves over cyclotomic fields. Number theory related to Fermat's last theorem (N. Koblitz, Ed.), Progress in Math., No. 26, Birkhäuser, Boston, Mass., 1982, 237-254.
Z519.14017; M84h:12017; R1986,4A396

RUDAZ S.,
[1] Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions. J. Math. Phys., 31 (1990), no. 12, 2832-2834.
Z729.11043; M91j:33012

RUDOLFER S.M., WILKINSON K.M.,
[1] A number-theoretic class of weak Bernoulli transformations, Math. Systems Theory, 7 (1973), 14-24.
Z258.10031; M48#2100; R1974,1V47

RUTGERS J.G.,
[1] Over de getallen en de polynomen van Stirling. Handel. Nederl. Natuur- en Geneesk. Congr., 11 (1907), 260-265.
J38.467

RUTKOWSKI J.,
[1] A $p$-adic analogue of the Legendre system. Number Theory, v. 2 (Budapest, 1987), 939-950. Colloq. Math. Soc. Janos Bolyai, 51 Amsterdam, 1990.
Z701.11064; M91h:11134

RUTKOWSKI J.: see also BARTZ K., RUTKOWSKI J.

RYBNIKOV K.A.,
[1] Introduction to combinatorical analysis, Moscow: Moscow State Univ., 1985, 2nd ed., 308 pp.
Z617.05001; M87b:05002; R1985,11V564K


SAALSCHÜTZ L.,
[1] Zwei Abhandlungen aus dem Gebiete der Bernoullischen Zahlen, Schrift. Phys.-ökonom. Gesell. Königsb. 33 (1892), 44-49.

[2] Verkürzte Recursionsformeln fü,r die Bernoullischen Zahlen, Zeit. für Math. und Phys., 37 (1892), 374-378.
J24.237

[3] Vorlesungen über die Bernoullischen Zahlen, ihren Zusammenhang mit den Secanten-Coefficienten und ihre wichtigeren Anwendungen, Springer-Verlag, Berlin, 1893. viii + 208 S.
J24.236

[4] Studien zu Raabe's Monographie über die Jacob Bernoullische Funktion, Zeit. für Math. und Phys., 42 (1897), 1-13.
J28.375

[5] Über Beziehungen zwischen den Anfangsgliedern von Differenzreihen und von deren Verwendung zu Summationen und zur Darstellung der Bernoullischen Zahlen, Schrift. Phys.-ökonom. Gesell. Königsb., 41 (1900), 14-17.

[6] Gleichungen zwischen den Anfangsgliedern von Differenzreihen und deren Verwendung zu Summationen und zur Darstellung der Bernoullischen Zahlen, J. Reine Angew. Math., 123 (1901), 210-240.
J32.280

[7] Die ganzen Potenzen der Cotangente und der Cosecante nebst neuen Formeln für die Bernoullischen Zahlen. Schriften der physik-ökonom. Ges. zu Königsberg i. Pr., 44 (1903), 32p.
J34.482

[8] Neue Formeln für die Bernoullischen Zahlen. J. Reine Angew. Math., 126 (1903), 99-101.
J34.482

SACHKOV V.N.,
[1] Combinatorical methods of discrete mathematics. (Russian) Moscow: Nauka, 1977, 319 pp.
R1978,4V321

[2] Probabilistic methods in combinatorical analysis. (Russian) Moscow: Nauka, 1978, 287 pp.
Z517.05011; M80g:05002; R1979,2V7

[3] Introduction to combinatorical methods of discrete mathematics. (Russian) Moscow: Nauka, 1982, 384 pp.
M85g:05001

SACHSE A.,
[1] Über die Darstellung der Bernoullischen und Eulerschen Zahlen durch Determinanten, Arch. für Math. und Phys., 68 (1882), 427-432.
J14.110,191

SAGAN B.E., ZHANG PING,
[1] Arithmetic properties of generalized Euler numbers, Southeast Asian Bull. Math. 21 (1997), no. 1, 73-78.
Z970.56656; M98h:11025

SAITO H.: see IBUKIYAMA T., SAITO H.

SALIÉ H.,
[1] Eulersche Zahlen, Sammelband zu Ehren des 250. Geburtstags Leonhard Eulers, Akademie-Verlag, Berlin, 1959, 293-310.
Z106,31; M24#A75; R1960,7814

[2] Arithmetische Eigenschaften der Koeffizienten einer speziellen Hurwitzschen Potenzreihe, Wiss. Z. Karl-Marx-Univ. Leipzig, Math.-Naturw. R., 12 (1963), 617-618.
Z117,277; M29#58

[3] Über die Koeffizienten Blasiusscher Reihen, Math. Nachr., 14 (1955), 241-248.
M18,379i; R1957,3757

SAMI Z.,
[1] On the first case of Fermat's last theorem, Glas. Mat. Ser. III, 21(41) (1986), no.2, 259-269.
Z621.10012; M88g:11012; R1987,12A82

[2] A sequence of numbers $a^m_{j,n}$, Glas. Mat. Ser. III, 23(43) (1988), no. 1, 3-13.
Z657.10009; M90f:11014; R1989,4B463

[3] On a sequence of polynomials, Proceedings of the Mathematical Conference in Pristina 1994, 39-46, Univ. Pristina, Pristina, 1995.
Z885.11022; M98h:11028

[4] Sequence $a\sp m\sb {j,n}$ and Bernoulli numbers. Proceedings of the Mathematical Conference in Pristina 1994, 47-50, Univ. Pristina, Pristina, 1995.
Z885.11019; M98h:11029

SANDHAM H.F.,
[1] Some infinite series, Proc. Amer. Math. Soc., 5 (1954), no. 3, 430-436.
M15-950f; R1955,3271

SÁNDOR I.,
[1] Remarks on Bernoulli polynomials and numbers, Stud. Cerc. Math., 41 (1989), no. 1, 47-49.
Z671.10009; M90h:11017

SANDS J. W.: see FRIEDMAN E., SANDS J. W.

SANKARANARAYANAN A.,
[1] An identity involving Riemann zeta function. Indian J. Pure Appl. Math., 18 (1987), no. 9, 794-800.
Z625.10031; M88i:11059; R1988,3A156

SANKARANARAYANAN A.: see RAMACHANDRA K., SANKARANARAYANAN A.

SARAFYAN D.: see OUTLAW C., SARAFYAN D., DERR L.

SASVÁRI Z.,
[1] An elementary proof of Binet's formula for the gamma function, Amer. Math. Monthly 106 (1999), no. 2, 156-158.

SATGÉ Ph.: see RIBET K. [3].

SATO M.,
[1] On formal fractions associated with the symmetric groups, J. Combin. Theory, Ser. A, 20 (1976), no. 1, 124-131.
Z335.10016; M52#13413; R1976,7V378

SATOH J.,
[1] $q$-analogue of Riemann's $\zeta$-function and $q$-Euler numbers, J. Number Theory, 31 (1989), no. 3, 346-362.
Z675.12010; M90d:11132

[2] The Iwasawa $\lambda\sb p$-invariants of $\Gamma$-transforms of the generating functions of the Bernoulli numbers, Japan. J. Math. (N.S.) 17 (1991), no. 1, 165--174.
Z739.11047; M92e:11122

[3] A construction of $q$-analogue of Dedekind sums. Nagoya Math. J., 127 (1992), 129-143.
Z761.11023; M93h:11022; R1976/77,5B12

[4] Construction of $q$-analogue by using Stirling numbers. Japan J. Math. (N.S.), 20 (1994), no. 1, 73-91.
Z808.11018; M95j:11015

[5] Sums of products of two $q$-Bernoulli numbers, J. Number Theory, 74 (1999), 173-180
Z916.11014; M99m:11019

SAUZET O.,
[1] Théorie d'Iwasawa des corps $p$-rationnels et $p$-birationnels, Manuscripta Math. 96 (1998), no. 3, 263-273.
Z905.11047; M99h:11123

SAVEL'EV L.Ya.,
[1] Combinatorics and probability. (Russian) Novosibirsk: Nauka, 1975, 423 pp.
Z447.05001; M52#13395; R1975,9V3K

SAYER F.P.,
[1] The sums of certain series containing hyperbolic functions. Fibonacci Quart., 14 (1976), no. 3, 215-223.
Z344.40002; M54#5663; R1976/77,5B12

SCAROWSKY M.,
[1] On a formal analogue of the Bernoulli numbers, J. Number Theory, 19 (1984), no. 2, 228-232.
Z546.10021; M86h:11019; R1985,8A110

SCHÄFFER J.J.,
[1] The equation $1^p+ 2^p+ 3^p+ \cdots +n^p = m^q$, Acta Math., 95 (1956), no. 3-4, 155-189.
Z71,37; M17-1187a; R1957,2878

SCHAPPACHER N., SCHOLL A.J.,
[1] The boundary of the Eisenstein symbol. Math. Ann., 290 (1991), no. 2, 303-321. Erratum: Math. Ann., 290 (1991), no. 4, 815.
Z729.11027; M93c:11037a/b

SCHARLAU W., OPOLKA H.,
[1] Von Fermat bis Minkowski. Eine Vorlesung über Zahlentheorie und ihre Entwicklung, Springer-Verlag, Berlin-New York, 1980. xi + 224pp.
Z426.10001*; M82g:10001; R1981,3A85K

[2] From Fermat to Minkowski. Lectures on the theory of numbers and its historical development. (Translation of [1]). Springer-Verlag, New York- Berlin, 1985, xi + 184 pp.
Z551.10001; M85m:11003; R1985,8A102K

SCHEIBNER W.,
[1] Zur Theorie der Maclaurinschen Summenformel, Berichte über die Verhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig, 9 (1857), 190-198.

SCHENDEL L.,
[1] Die Bernoullischen Funktionen und das Taylorsche Theorem nebst einem Beitrag zur analytischen Geometrie der Ebene in trilinearen Coordinaten, H. Costenoble, Jena, 1876.
J8.133

[2] Zur Theorie der Reihen, Zeit. für Math. und Phys., 16 (1871), 211-227.
J3.105

SCHERK H.F.,
[1] Über einen allgemeinen, die Bernoullischen Zahlen und die Coëfficienten der Secantenreihe zugleich darstellenden Ausdruck, J. Reine Angew. Math., 4 (1829), 299-304.

[2] Von den numerischen Coeffizienten der Secantreihe, ihrem Zusammenhange, und ihrer Analogie mit den Bernoullischen Zahlen. Gesammelte Mathematische Abhandlungen, Reimer, Berlin, 1825, 1-30.

SCHIKHOF W.H.,
[1] Ultrametric calculus. An introduction to $p$-adic analysis. Cambridge University Press, Cambridge-New York, 1984. viii+306 pp.
Z553.26006; M86j:11104

SCHINZEL A.,
[1] Sur les nombres composés $n$ qui divisent $a^n - a$, Rend. Circ. Mat. Palermo (2), 7 (1958), no. 1, 37-41.
Z83,261; M21#4935; R1959,9761

SCHINZEL A., URBANOWICZ J., VAN WAMELEN P.,
[1] Class numbers and short sums of Kronecker symbols, J. Number Theory 78 (1999), no. 1, 62-84.

SCHLÄFLI L.,
[1] On Staudt's theorem relating to the Bernoullian numbers, Quart. J. Math., 6 (1864), 75-77.

SCHLÖMILCH O.,
[1] Über die Bernoullischen Zahlen und die Coëfficienten der Secantreihen, Arch. für Math. und Phys., 1 (1841), 360-363.

[2] Über die recurrirende Bestimmung der Bernoullischen Zahlen, Arch. für Math. und Phys., 3 (1843), 9-18.

[3] Développement d'une formule qui donne en mème temps les nombres de Bernoulli et les coëfficients de la série qui exprime la sécante, J. Reine Angew. Math., 32 (1846), 360-364.

[4] Relation zwischen den Facultätencoefficienten, Arch. für Math. und Phys., 9 (1847), 333-335.

[5] Über die Summe der Reihe $1^m + \cdots + z^m$, Arch. für Math. und Phys., 10 (1847), 342-344.

[6] Theorie der Differenzen und Summen. Druck und Verlag von H.W. Schmidt, Halle, 1848, 241 pp.

[7] Neue Methode zur Summirung endlicher und unendlicher Reihen, Arch. für Math. und Phys., 12 (1849), 130-166.

[8] Neue Formeln zur independenten Bestimmung der Sekanten und Tangenten Coëfficienten, Arch. für Math. und Phys., 16 (1851), 411-418.

[9] Handbuch der algebraischen Analysis, 2te Auflage. Druck und Verlag von Fr. Frommann, Jena, 1851. viii + 344 pp.

[10] Über die independente Bestimmung der Coëfficienten unendlicher Reihen und der Facultätencoefficienten insbesondere, Arch. für Math. und Phys., 18 (1852), 306-327.

[11] Über die Bernoulli'schen Funktion und deren Gebrauch bei der Entwickelung halbconvergenter Reihen, Zeit. für Math. und Phys. (2), 1 (1856), 193-211.

[12] Über ein allgemeines Princip für Reihenentwickelungen, Zeitsch. für Math. und Phys., 2 (1857), 289-298.

[13] Über die Lambert'sche Reihe, Zeit. für Math. und Phys. (2), 6 (1861), 407-415.

[14] Compendium der höheren Analysis. Band 2. Braunschweig, 1862.

[15] Die Bernoulli'schen Funktionen und die halbconvergenten Reihen, Compendium der höheren Analysis, II (1874), 207-238.

SCHMIDT C.G.,
[1] The p-adic L-functions attached to Rankin convolutions of modular forms, J. Reine Angew. Math., 368 (1986), 201-220.
Z585.10020; M88e:11038; R1986,12A586

SCHMIDT H.,
[1] Asymptotische Entwicklung von verallgemeinerten Bernoullischen Funktionen und von Teilsummen Dirichletscher Reihen mit periodischer Koeffizientenfolge, Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, III, J. Reine Angew. Math., 274/275 (1975), 94-103.
Z312.10027; M52#303; R1975,12A143

[2] Zur Theorie und Anwendung Bernoulli-Nörlundscher Polynome und gewisser Verallgemeinerungen der Bernoullischen und der Stirlingschen Zahlen, Arch. Math. (Basel), 33 (1979), no. 4, 364-374.
Z438.10011; M81i:10017; R1980,11V460

SCHMIDT M.: see BUTZER P.L. et al.

SCHMIDT P.,
[1] The Stickelberger element of an imaginary quadratic field, Acta Math. 91 (1999), no. 2, 165-169.

SCHMIT C.: see BALAZS N.L., SCHMIT C., VOROS A.

SCHMITZ E.,
[1] Asymptotic expansions for the coefficients of $e^{P(z)}$, Bull. London Math. Soc., 21 (1989), 482-486.

SCHNEIDER P.,
[1] Über die Werte der Riemannschen Zeta-funktion an den ganzzahligen Stellen, J. Reine Angew. Math., 313 (1980), 189-194.
Z422.10030; M82g:10057; R1980,8A120

SCHOENBERG I.J.,
[1] Norm inequalities for a certain class of $C\sp{\infty }$ functions, Israel J. Math. 10 (1971), 364-372.
Z229.26019; M45 #3661

[2] The elementary cases of Landau's problem of inequalities between derivatives, Amer. Math. Monthly, 80 (1973), no. 2, 121-158.
Z261.26014; M47#3619; R1973,8B56

[3] Cardinal spline interpolation. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. vi+125 pp.
Z264.41003; M54 #8095

[4] On the remainders and the convergence of cardinal spline interpolation for almostperiodic functions. Studies in spline functions and approximation theory, pp. 277-303. Academic Press, New York, 1976.
Z338.41007; M58 #1838

SCHOENEBERG B.,
[1] Elliptic modular functions. Springer-Verlag, New York-Heidelberg, 1974. viii + 233 pp.
Z285.10016*; M54#236; R1975,5A640K

SCHOENFELD L.: see BERNDT B.C., SCHOENFELD L.

SCHOFF R.,
[1] The structure of the minus class groups of abelian number fields. University of Utrecht, Preprint No. 588, Oct. 1989.

SCHOISSENGEIER J.,
[1] Der numerische Wert gewisser Reihen, Manuscr. Math., 38 (1982), no. 2, 257-263.
Z499.10013; M83i:10039; R1983,1A82

[2] Der numerische Wert gewisser Reihen, Lecture Notes in Mathematics, No. 1114, 143-147, Springer-Verlag, Berlin-Heidelberg-New York, 1985.
Z557.10013; R1985,11A129

[3] Abschätzung für $\sum_{n\leq N}B_1(n\alpha)$, Monatsh. Math., 102 (1986), no. 1, 59-77.
Z613.10011; M87j:11020; R1987,3A168

[4] Eine explizite Formel für $\sum_{n \leq X}B_2(\{n\alpha\)$. In: Zahlentheoretische Analysis II. Seminar, 1984-86, pp. 134-138. Lecture Notes in Mathematics No. 1262, Springer-Verlag, Berlin - Heidelberg - New York, 1987.
Z622.10007; M90j:11021; R1988,3A199

SCHOISSENGEIER J.: see also HLAWKA E., SCHOISSENGEIER J., TASCHNER R.

SCHOLL A.J.: see SCHAPPACHER N., SCHOLL A.J.

SCHONBACH D.I.: see NEUMAN C.P., SCHONBACH D.I.

SCHÖNHAGE A.: see ODLYZKO A.M., SCHÖNHAGE A.

SCHRÖDER E.,
[1] Verallgemeinerung von Maclaurins Summenformel und Bernoullische Funktionen, Zürich, 1867.

[2] Neueres über Bernoullische Functionen von natürlicher Ordnungszahl, Verhandl. Gesellschaft deutscher Naturforscher und Ärzte, Bremen, 15. - 20. September 1890, 5-6.
J22.270

SCHOOF R.,
[1] Minus class groups of the fields of the $l$th roots of unity, Math. Comp., 67 (1998), no. 223, 1225-1245.
View or retrieve article
Z980.24860; M98j:11085

SCHROTH P.,
[1] Characterization of the Bernoulli-polynomials, $\exp$ and $\psi$ by Nörlund's multiplication formula, Period. Math. Hung., 12 (1981), no. 3, 191-204.
Z445.39002; M83j:39001; R1982,3B12

SCHULTZ H.J.,
[1] The sum of the $k$-th power of the first $n$ integers. Amer. Math. Monthly, 87 (1980), no. 6, 478-481.
Z445.05006; M82c:05014; R1981,7B565

SCHÜTZENBERGER M.-P.: see FOATA D., SCHÜTZENBERGER M.-P.

SCHWARTZ L.: see BAKER A.J. et al.

SCHWARZ S.,
[1] Algebraic Numbers, (Slovak), Prague, 1950.
Z41,011*; M14-22f

SCHWATT I.J.,
[1] An Introduction to the Operations with Series, Philadelphia, 1924, (s. W. Sierpinski, Rachunek rózniczkowy, Warszawa, 1947).
J50.151

[2] The sum of like powers of a series of numbers forming an arithmetical progression and the Bernoulli numbers, Mat. sbornik, 39 (1932), no. 4, 134-140.
Z7,070; J58.I.93

[3] Finite expressions for the Bernoulli numbers obtained by the actual expansion of trigonometric functions by Maclaurin's theorem, J. Math. Pures Appl. (9), 11 (1932), 143-151.
Z5,014; J58.I.93

[4] Independent expressions for the Bernoulli numbers. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 261-262.
J(48.255)

[5] Independent expressions for the Euler numbers. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 262.
J(48.255)

[6] Independent expressions for the Euler numbers of Higher Order. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 262.
J(48.255)

[7] Relations involving the numbers of Bernoulli and Euler (Abstract). Bull. Amer. Math. Soc., 27 (1921), 262.
J(48.255)

[8] Expressions for the Bernoulli function of order $p$. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 348.
J(48.255)

[9] The values of $\sum_{k=1}^n\sum_{a=1}^{2k} \tan^p a\pi /(2k+1),\; \sum_{k=1}^\infty \prod_{a=1}^{2k} {\rm ctn}^p a\pi(2k+1)$, and similar forms in terms of Bernoulli and Eulerian numbers. (Abstract). Bull. Amer. Math. Soc., 29 (1923), 151.
J(49.161)

[10] Expressions for the Euler numbers obtained by expanding $\sec x$ by means of Maclaurin's Theorem. Math. Z., 31 (1930), 151-158.
J55.I.135

[11] Certain expansions involving the Bernoulli numbers. Giornale di Mat., 67 (1929), 162-167.
J55.I.216

SCHWERING K.,
[1] Zur Theorie der Bernoulli'schen Zahlen, Math. Ann., 52 (1899), no. 1, 171-173.
J30.253

SCOVILLE R.: see CARLITZ L., SCOVILLE R.

SCZECH R.,
[1] Zur Summation von L-Reihen, Bonner Math. Schriften, 1982, No. 141.
Z492.10035; M84m:12015; R1983,4B134

[2] Eisenstein cocylces for $GL_2 Q$ and values of $L$-functions in real quadratic fields. Comment. Math. Helv., 67 (1992), no. 3, 363-382.
Z776.11021; M93h:11047

[3] Eisenstein group cocyles for $GL_n$ and values of $L$-functions. Invent. Math., 113 (1993), no. 3, 581-616.
Z809.11029; M94j:11049

SEGAL R.S.,
[1] Application of Bernoulli polynomials to the theory of cyclotomic fields, Ph.D. Thesis, MIT, 1965.

[2] Generalized Bernoulli numbers and the theory of cyclotomic fields, Acta. Math., 121 (1968), 48-75.
Z164,58; M38#133; R1969,3A126

SEIDEL P.L. von,
[1] Über eine einfache Entstehungsweise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungs. Akad. Wiss. München, Mat.-Phys. Kl., 7 (1877), 157-187.

SELBERG A.: see BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.

SELFRIDGE J.L., NICOL C.A., VANDIVER H.S.,
[1] Proof of Fermat's Last Theorem for all prime exponents less than 4002, Proc. Nat. Acad. Sci. U.S.A., 41 (1955), no. 11, 970-973.
Z65,273; M17-348a; R1956,7085

SELIWANOFF D.,
[1] Lehrbuch der Differenzenrechnung. Leipzig, 1904.
J35.346

SELUCKÝ K., SKULA L.,
[1] Irregular imaginary fields, Arch. Math. (Brno), 17 (1981), 95-112.
Z476.12005; M84a:12015; R1982,2A163

SEREBRENIKOV S.Z.,
[1] Tablitsy pervykh devyanosta chisel Bernulli [Tables of the first ninety Bernoulli numbers]. Zap. Akad. Nauk, Sankt Peterburg, 16 (1905), no. 10, 1-8.
J36.342

[2] Novyi sposob vychisleniya chisel Bernulli [A new method of computation of Bernoulli numbers]. Zap. Akad. Nauk, Sankt Peterburg, 19 (1906), 1-6.
J38.324

SERRE J.P.,
[1] Cours d'arithmétique, Paris, 1970, Ch.7.
Z225.12002*; M41#138; R1971,7A102K

[2] Formes modulaires et fonctions zêta p-adiques. In: Modular functions of one variable, III, Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972, 191-268, Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973.
Z292.00007*; M53#7949a; R1974,6A446

[3] Sur le residu de la fonction zêta p-adique d'un corps de nombres, C.R. Acad. Sci., Paris, 287A (1978), 183-188.
Z393.12026; M58#22024; R1979,2A259

SERRET J.-A.,
[1] Sur l'évaluation approchée du produit $1. 2. ... .x$ lorsque $x$ est un très-grand nombre, et sur la formule de Stirling, C.R. Acad. Sci., Paris, 50 (1860), 662-666.

SHAFAREVICH I.R.,
[1] Zeta-function. Lecture Notes 1966/67. (Russian) Moscow State Univ., 1969.
R1969,12A249

[2] Selected chapters of algebra (Russian), Matem. obrazovanie, 1997, no. 2, 3-33.

SHAFAREVICH I.R.: see also BOREVICH Z.I., SHAFAREVICH I.R.

SHAH K.N.,
[1] Explicit formulas for $\sum_{i=1}^ri^r (\equiv S_r)$ and Bernoulli's numbers $B_r$, Vidya, B 15 (1972), no. 2, 106-117.
M52#5552

SHANK H.S.: see DICKEY L.J., KAIRIES H.H., SHANK H.S.

SHANK H.S.: see GRANVILLE A., SHANK H.S.

SHANKS D.,
[1] Solved and unsolved problems in number theory, Vol. 1. Spartan Books, Washington, 1962. xi + 229 pp.
Z116,30; M28#3952

[2] Generalized Euler and class numbers, Math. Comp., 21 (1967), 689-694.
Z164,51; M36#6343; R1968,8A118

SHANKS E.B.,
[1] Iterated sums of powers of the binomial coefficients, Amer. Math. Monthly, 58 (1951), 404-407.
Z43,12; M13-899f

[2] A finite formula for the Bernoulli numbers, Amer. Math. Monthly, 59 (1952), 496.

SHANNON A.G.,
[1] Fibonacci analogs of the classical polynomials, Math. Mag., 48 (1975), 123-130.
Z306.33005; M51#6000; R1976,3V518

[2] Jackson's calculus of sequences and Bernoulli polynomials. Bull. Number Theory Related Top., 13 (1989), no. 1-3, 7-16.
Z745.11017; M93f:11019

SHANNON A.G.: see also HORADAM A.F., SHANNON A.G.

SHANNON A.G.: see also MELHAM R.S., SHANNON A.G.

SHARMA A.,
[1] q-Bernoulli and Euler numbers of higher order, Duke Math. J., 25 (1958), 343-353.
Z102,31; M20#2479; R1969,6619

SHEPPARD W.F.,
[1] On the relation between Bernoulli and Euler numbers, Quart. J. Math., 30 (1899), 18-46.
J29.376

[2] The power-sum formula and Bernoullian function, Math. Gaz. 6 (1912), 332-336.
J43.337

[3] The power-sum formula and the Bernoullian functions. III. The Euler-Maclaurin formula. Math. Gaz., 7 (1913), 100-104.
J44.514

SHERWOOD H.,
[1] Sums of powers of integers and Bernoulli numbers, Math. Gaz., 54 (1970), no. 389, 272-274.
Z206,56; M58#10708; R1971,5B341

SHEVELEV V.S.,
[1] On an arithmetic property of permutation numbers with a given signature associated with the Morse sequence (Russian), Izv. Vyssh. Uchebn. Zaved. Sev.-Kavk. Reg. Estestv. Nauki 1996, no. 2, 20-24, 98-99.
M99e:11023

SHIMADA T.,
[1] Fermat quotient of cyclotomic units. Acta Arith. 76 (1996), no. 4, 335--358.
Z867.11076; M97k:11147

SHINTANI T.,
[1] On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 23 (1976), no.2, 393-417.
Z349.12007; M55#266; R1977,4A117

[2] On Kronecker limit formula for real quadratic fields, Proc. Japan Acad., 52 (1976), no. 7, 355-358.
Z359.12004; M58#596; R1977,5A95

[3] On a Kronecker limit formula for real quadratic fields, J. Fac. Sci. Univ. Tokyo, Ser. IA, Math., 24 (1977), no. 1, 167-199.
Z364.12012; M57#12012; R1977,12A136

SHIRATANI K.,
[1] On some relations between Bernoulli numbers and class numbers of cyclotomic fields, Mém. Fac. Sci. Kyushu Univ., Ser. A, 18 (1964), 127-135.
Z148,28; M30#3086; R1966,1A137

[2] Ein Satz zu den Relativklassenzahlen der Kreiskörper, Mém. Fac. Sci. Kyushu Univ., 21 (1967), 132-137.
Z189,53; M35#6648; R1968,5A188

[3] A generalization of Vandiver's congruence, Mém. Fac. Sci. Kyushu Univ., 25 (1971), 144-151.
Z252.12008; M46#5289; R1972,1A595

[4] Kummer's congruence for generalized Bernoulli numbers and its application. Seminar on Modern Methods in Number Theory, Paper No. 31, 7 pp., Inst. Statist. Math., Tokyo, 1971.
Z307.12014; M51#10215

[5] Kummer's congruence for generalized Bernoulli numbers and its application, Mém. Fac. Sci. Kyushu Univ., 26 (1972), 119-138.
Z243.12009; M50#12976

[6] On Euler numbers, Mem. Fac. Sci. Kyushu Univ. Ser. A, 27 (1973), 1-5.
Z267.10009; M47#3307; R1973,11V429

[7] On certain values of p-adic L-functions, Mém. Fac. Sci. Kyushu Univ., 28 (1974), 59-82.
Z313.12005; M53#8022; R1975,2A400

[8] On a formula for p-adic L-functions, J. Fac. Sci. Univ. Tokyo, Ser. 1A, Math., 24 (1977), 45-53.
Z362.12014; M56#320; R1977,12A367

[9] On $p$-adic zeta-functions of the Lubin-Tate groups. Kyushu J. Math., 48 (1994), no. 1, 55-62.
Z818.11045; M95g:11117; R1996,7A224

SHIRATANI K., IMADA T.,
[1] The exponential series of the Lubin-Tate groups and $p$-adic interpolation. Mem. Fac. Sci. Kyushu Univ. Ser. A, 46 (1992), no. 2, 351-365.
Z777.11050; M94f:11123

SHIRATANI K., YAMAMOTO S.,
[1] On a p-adic interpolation function for the Euler numbers and its derivative, Mem. Fac. Sci. Kyushu Univ. Ser. A, 39 (1985), no. 1, 113-125.
Z574.12017; M87f:11099; R1985,12A321

SHIRATANI K., YOKOYAMA S.,
[1] An application of p-adic convolutions, Mém. Fac. Sci. Kyushu Univ., Ser. A, 36 (1982), no. 1, 73-83.
Z574.12017; M83m:10011; R1983,1A343

SHIRATANI K.: see also ISHIBASHI M., SHIRATANI K.

SHIRATANI K.: see also KANEMITSU S., SHIRATANI K.

SHOJI T.: see AGOH T., SHOJI T.,

SHOKROLLAHI M.A.,
[1] Stickelberger codes, Des. Codes Cryptogr. 9 (1996), no. 2, 203-213.
Z866.94022; M98d:94039

[2] Relative class number of imaginary abelian fields of prime conductor below 10000, Math. Comp. 68 (1999), no. 228, 1717-1728.
M99m:11147

SHOVELTON S.T.,
[1] An elementary proof of Staudt's theorem on Bernoulli's numbers, Messeng. Math., 44 (1914), 24-25.
J45.1244

SHTOKALO I.Z.: see POGREBISSKII I.B., SHTOKALO I.Z.

SHUKLA R.N., MISHRA S.S.,
[1] Some important theorems on multivariate Bernoulli polynomials of second kind. (Hindi) Vijnana Parishad Anusandhan Patrika 38 (1995), no. 3, 211-217.
M97g:05006

SHUKLA R.N.: see also MISRA S.S., SHUKLA R.N.

SHU LINGHSUEH,
[1] Kummer's criterion over global function fields, J. Number Theory, 49 (1994), no. 3, 319-359.
Z816.11036; M96c:11134

SIDLER G.,
[1] Über eine algebraische Reihe, Mittheil. Naturf. Gesell., Bern, 1899 (1900), 13-32.
J30.252

SIEBERT H.: see KIMURA N., SIEBERT H.

SIEGEL C.L.,
[1] Zu zwei Bemerkungen Kummers, Nachr. Akad. Wiss. Göttingen, Math. -Phys. Kl. II, (1964), no. 6, 51-57.
Z119,277; M29#1198; R1967,8A102

[2] Über die Fourierschen Koeffizienten der Eisensteinschen Reihen, Det. Kgl. Danske Videns. Selskab., Math-fys. Meddel., 34 (1964), 1-20.
Z132,64; M30#1984; R1966,6A84

[3] Beweis einer Formel für die Riemannsche Zetafunktion, Math. Scand. 14 (1964), 193-196.
Z137.25801; M31#2219

[4] Bernoullische Polynome und quadratische Zahlkörper, Nachr. Akad. Wiss. Göttingen (2), Math.-Phys. Kl., (1968), no. 2, 7-38.
Z273.12002; M38#2123

[5] Berechnung von Zetafunktionen an ganzzahligen Stellen, Nachr. Akad. Wiss. Göttingen (2), Math.-Phys. Kl. II, (1969), no. 10, 87-102.
Z186,88; M40#5570; R1972,11A85

SIEGEL C.L.: see also BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.

SILVERMAN J.H.,
[1] The arithmetic of elliptic curves, Springer-Verlag, New York etc., 1986, vii + 400 pp. (Graduate Texts in Math., No. 106).
M87g:11070; R1986,8A420K

SILVERMAN L.L.,
[1] Functional generalization of Bernoulli numbers, Riveon Lematematika, 7 (1954), 33-37. (Hebrew. English summary.)
M15-400j; R1955,5612

SIMALARIDES A.,
[1] Congruences mod $p^n$ for the Bernoulli numbers, Fibonacci Quart. 36 (1998), no. 3, 276-281.
M99e:11024

SIMMONS G.F.,
[1] Calculus gems. Brief lives and memorable mathematics. McGraw-Hill, Inc., New York, 1992, xvi+355 pp.
Z846.01012; M94m:01036

SIMONDS E.F.,
[1] The coefficients of the series for $\tan x$. Math. Gaz., 19 (1935), 37-39.
J61.I.66; Z11.108

SINGH A.: see GANDHI J.M., SINGH A.

SINGH D.,
[1] The numbers $L(m,n)$ and their relations with prepared Brenoullian and Eulerian numbers, Math. Student, 20 (1952), 66-70.
Z49,309; M14-727f

[2] On the divisibility of Eulerian and prepared Bernoullian numbers by prime numbers, Math. Student, 20 (1952), 71-73.
Z49,309; M14-728a

SINGH R., PRASAD S.,
[1] An extension of the Bernoulli and Euler polynomials, Jñanabha, 20 (1990), 7-12.
Z727.33011; M92b:11011

SINGH S.N.,
[1] On unification and extension of Bernoulli, Euler and Eulerian polynomials. Proc. National Symposium on Special Functions and Their Applications (Gorakhpur,1986), 163-171, Univ. Gorakhpur.
M91e:11023

SINGH S.N., MISHRA S.S.,
[1] On the extension of Bernoulli, Euler and Eulerian polynomials. Tamkang J. Math. 27 (1996), no. 3, 189-199.
Z873.11017; M98e:11022

SINGH S.N., RAI B.K.,
[1] Characterization of the Appell set $D_n(x;a,k)$, Indian J. Pure Appl. Math., 13 (1982), no.5, 601-605.
Z502.33008; M83g:33010; R1982,11B57

[2] Properties of some extended Bernoulli and Euler polynomials, Fibonacci Quart., 21 (1983), no. 3, 162-173.
Z529.10016; M85f:05005

[3] An Appell cross-sequence suggested by Bernoulli and Euler polynomials, Rev. Roumaine Math. Pures Appl., 33 (1988), no. 7, 613-621.
Z649.33004; M89i:05030; R1989,2B27

SINGH S.N., RAI B.K., RAI V.S.,
[1] An extension of Bernoulli and Euler polynomials, Ganita, 2 (1982), no. 2, 108-112.
Z585.33011; M85k:33012

SINGH S.N., SINGH V.P., RAI B.K.,
[1] A characterization of some extended Bernoulli and Euler polynomials, Vijnana Parishad, Anusandhan Patrika, 26 (1983), no. 2, 61-64.
M85b:11016

SINGH S.N.: see also HUSSAIN M.A., SINGH S.N.

SINGH S.N.: see also RAI B.K. et al.

SINGH S.N.: see also RAI V.S., SINGH S.N.

SINGH V.P.: see SINGH S.N., SINGH V.P., RAI B.K.

SINGHOF W.,
[1] Einige Beziehungen zwischen stabiler Homotopietheorie und Zahlentheorie, Jahresber. Deutsch. Math.-Verein., 91 (1989), no. 2, 55-66.
Z702.55012; M90d:55023; R1989,9A444

SINIGALLIA L.,
[1] Sui nuovi numeri pseudo-Euleriani del Prof. Pascal. Rend. Palermo, 24 (1907), 223-228.
J38.467

[2] Una extensione dei numeri Bernoulliani. Rend. Palermo, 25 (1908), 20-35.
J39.502

SINNOTT W.,
[1] On the $\mu$-invariant of the $\Gamma$-transform of a rational function, Invent. Math., 75 (1984), no. 2, 273-282.
Z531.12004; M85g:11112; R1984,8A294

SINNOTT W.: see also COATES J., SINNOTT W.

SINTSOV D.M.,
[1] O funktsiyakh Bernulli drobnykh poryadkov [On Bernoulli functions of fractional orders]. Izvestiya Kazansk. fiz.-mat. obshchestva (1), 8 (1890), 291-336.
J22.443

[2] Bernullievy funktsii s proizvol'nymi ukazatelyami [Bernoulli functions with arbitrary indices]. Izvestiya Kazansk. fiz.-mat. obshchestva (2), 1 (1891), no. 2, 234-256.
J24.404

[3] Razlozhenie proizvol'nykh stepenej trigonometricheskikh funktsij v stepennye stroki [Expansion of arbitrary powers of trigonometrical functions in power series]. Izvestiya Kazansk. fiz.-mat. obshchestva (2), 4 (1894), no. 4, 199-204.
J26.471

[4] Zametka o chislakh Bernulli [A note on Bernouli numbers]. Izvestiya Kazansk. fiz.-mat. obshchestva (2), 8 (1898), no. 2, 104-106.
J29.221

SITARAMACHANDRA RAO R., DAVIS B.,
[1] Some identities involving the Riemann zeta-function. II. Indian J. Pure Appl. Math., 17 (1986), no. 10, 1175-1186.
Z614.10013; M88d:11080; R1987,6B39

[2] Behaviour of $log {\eta}(\tau)$ at a rational point, Indian J. Pure Appl. Math., 18 (1987), no. 2, 111-121.
Z611.10015; M88j:11026; R1987,9A91

SITARAMACHANDRA RAO R.: see KANEMITSU S., SITARAMACHANDRA RAO R.

SITARAMAN S.,
[1] Vandiver revisited. J. Number Theory 57 (1996), no. 1, 122-129.
Z855.11057; M97a:11170

SKORUPPA N.-P.,
[1] Developments in the theory of Jacobi forms. Max-Planck-Institut für Math., Bonn, MPI/89-40, 17 pp.
Z745.11029; M92e:11043

[2] Binary quadratic forms and the Fourier coefficients of elliptic and Jacobi modular forms. Max-Planck-Institut für Math., Bonn, MPI/89-57, 32 pp.
Z709.11028; M91j:11030

[3] Computations of Siegel modular forms of genus two. Math. Comp., 58 (1992), no. 197, 391-398.
Z749.11030; M92e:11041

SKULA L.,
[1] Non-possibility to prove infinity of regular primes from some theorems, J. Reine Angew. Math., 291 (1977), 162-181.
Z338.10013; M56#5413; R1977,12A141

[2] On certain ideals of the group ring $ Z[G]$, Arch. Math. (Brno), 15 (1979), no.1, 53-56.
Z435.12006; M81f:12007; R1980,3A278

[3] Index of irregularity of a prime, J. Reine Angew. Math., 315 (1980), 92-106.
Z419.10016; M81c:12014; R1980,12A137

[4] A remark on Mirimanoff polynomials, Comment. Math. Univ. St. Paul. (Tokyo), 31 (1982), no.1, 89-97.
Z496.10006; M84b:10022

[5] System of equations depending on certain ideals, Arch. Math. (Brno), 21 (1985), 23-38.
Z589.12005; M87g:11033; R1986,4A421

[6] Systems of Kummer's and Mirimanoff's congruences, Summer School on Number Theory, held at Chlébské, Sept. 1983, Brno, 1985, 44-51.
Z648.10012

[7] A note on the index of irregularity, J. Number Theory, 22 (1986), 125-138.
Z589.12006; M87d:11080; R1986,8A324

[8] On the Kummer's system of congruences, Comment. Math. Univ. St. Paul., 36 (1986), no. 2, 137-163.
Z604.10006; M87m:11016; R1987,12A83

[9] Fermat's last theorem and the Fermat quotients. Conference report of the 9th Czechoslovak Colloquium on Number Theory held at Rackova Dolina, Sept. 1989. pp. 78-86. Masaryk University, Brno, 1990.
Z697.10003*

[10] Some consequences of the Kummer system of congruences, Comm. Math. Univ. St. Paul., 39 (1990), no. 1, 19-40.
Z701.11010; M91i:11030; R1991,8A123

[11] Fermat's last theorem and the Fermat quotients. Comm. Math. Univ. St. Paul., 41 (1992), no. 1, 35-54.
Z753.11016; M93f:11028; R1993,7A135

[12] The Kummer system of congruences and index of irregularity. Österr.-Ung.-Slow. Koll. über Zahlentheorie Graz- Mariatrost, 1992. Grazer Math. Ber., 318 (1992), 169-172.
Z796.11004; M94h:11024; R1993,11A133

[13] Some bases of the Stickelberger ideal. Math. Slovaca, 43 (1993), no. 5, 541-571.
Z798.11044; M95e:11117; R1996,2A163

[14] The orders of solutions of the Kummer system of congruences. Trans. Amer. Math. Soc., 343 (1994), no. 2, 587-607.
Z810.11015; M94h:11025; R1995,3A101

[15] Nekteré historické aspekty Fermatova problému (Some historical aspects of Fermat's problem). Pokroky Mat. Fyz. Astronom., 39 (1994), no. 6, 318-330.
Z831.11025; M95k:11002

[16] Agoh's bases of the Stickelberger ideal, Math. Slovaca, 44 (1994), no. 5, 663-670.
Z826.11049; M96c:11123

[17] On a special ideal contained in the Stickelberger ideal, J. Number Theory, 58 (1996), no. 1, 173-195.
Z861.11063; M97d:11157

[18] Fermat and Wilson quotients for $p$-adic integers, Acta Math. Inform. Univ. Ostraviensis, 6 (1998), 167-181.

SKULA L., SLAVUTSKII I.SH.,
[1] Bernoulli Numbers. Bibliography (1713-1983). J.E. Purkyne Univ., Brno, 1988.
Z637.10001; M89i:11002

SKULA L.: see also AGOH T., SKULA L.

SKULA L.: see also AGOH T., DILCHER K., SKULA L.

SKULA L.: see also DILCHER K., SKULA L.

SKULA L.: see also SELUCKÝ K., SKULA L.

SLAVUTSKII I.SH.,
[1] Ratsionalizatsiya formul Dirikhle dlya chisla klassov idealov veshchestvennogo kvadratichnogo polya [Rationalization of the Dirichlet formulae for the number of classes of ideals of a real quadratic field]. Trudy 7 nauchn. konf. Khabarovsk. Gos. Pedagogichesk. instituta, (1959), 50-52.

[2] On the class-number of the ideals of a real quadratic field. (Russian). Izv. Vyssh. Uchebn. Zaved. Matematika, 1960 (1960), no. 4(17), 173-177.
Z99,26; M24,A1905; R1962,3A219

[3] Ob arifmeticheskoj strukture L-funktsij Dirikhle [On the arithmetical structure of Dirichlet L-functions]. Trudy 8 nauchn. konf. Khabarovsk. Gos. Pedagogichesk. instituta, (1961), 125-127.

[4] Nekotorye sravneniya dlya chisla klassov veshchestvennogo kvadratichnogo polya s prostym diskriminantom [Some congruences for the class number of a real quadratic field with prime discriminant]. Uch. zap. Leningradsk. Gos. Pedagogichesk. instituta, 218 (1961), 179-189.
Z138,32; R1962,4A113

[5] Generalized Voronoi-Grün congruence and the class number of an imaginary quadratic field. (Russian). Trudy Nauchn. Ob'ed. Prepodav, Fiz.-Mat. Fak. Ped. Inst. Dal'n. Vostok., Mat. 1 (1962), 82-84.
M35#4191; R1964,7A172

[6] Chislo klassov idealov absolyutno abeleva polya i obobshchennye chisla Bernulli [The number of classes of ideals of an absolute abelian field and generalized Bernoulli numbers]. Trudy Nauchn. Ob'ed. Prepodav, Fiz.-Mat. Fak. Ped. Inst. Dal'n. Vostok., Mat. 3 (1963), 75-80.
R1965,9A236

[7] On irregular primes, (Russian) Acta Arith., 8 (1962/1963), 123-125.
Z113,262; M27#2475; R1964,2A173

[8] An estimate from above and the arithmetical calculation of the class-number of real quadratic fields, (Russian) Izv. Vyssh. Uchebn. Zaved. Matematika, (1965), no. 2(45), 161-165.
Z126,275; M32#2400; R1965,9A103

[9] On Mordell's theorem, Acta Arith., 11 (1965), 57-66.
Z132,283; M31#159; R1966,91A130

[10] Generalized Voronoi congruence and the number of classes of ideals of an imaginary quadratic field, II, (Russian). Izv. Vyssh. Uchebn. Zaved. Matematika, (1966), no. 4(53), 118-126.
Z146,278; M35#4192; R1966,12A279

[11] L-functions of a local field, and a real quadratic field, (Russian) Izv. Vyssh. Uchebn. Zaved. Matematika, (1969), no. 2(81), 99-105.
Z188,348; 507.12009; M40#4240; R1969,7A293

[12] The simplest proof of Vandiver's theorem, Acta. Arith., 15 (1969), 117-118.
Z198,74; M38#5745; R1969,10A78

[13] On the number of classes of ideals and the fundamental unit of a real quadratic field, (Russian) Akad. Nauk Kazakh. SSR, Alma-Ata, (1969), 73-70.
M52#10558

[14] Chislo klassov idealov absolyutno abeleva polya i lokal'nye dzeta-funktsii [The number of classes of ideals of an absolute abelian field and local zeta functions]. X Vsesoyuzn. algebraichesk. kollokvium, Rezyume soobshch. i dokl., Novosibirsk, 2 (1969), 160-162.

[15] O chisle klassov absolyutno abeleva polya [On the class number of an absolute abelian field]. XI Vsesoyuzn. algebraichesk. kollokvium, Rezyume soobshch. i dokl., Kishinev, (1971), 331-332.

[16] Generalized Bernoulli numbers that belong to unequal characters, and an extension of Vandiver's theorem, (Russian) Leningrad. Gos. Ped. Inst. Uchen. Zap., 496 (1972), no. 1, 61-68.
M46#7194; R1972,7A137

[17] Local properties of Bernoulli numbers and a generalization of the Kummer-Vandiver theorem, (Russian). Izv. Vys. Uchebn. Zaved. Matematika., 1972, no. 3(118), 61-69.
Z244.12006; M46#151; R1972,7A287

[18] On the Nagell-Estermann theorem, (Russian) Vil. Gos. Univ., Vilnius, (1974), 235-236.
M51#5462

[19] Square-free numbers and a quadratic field, (Russian). Colloq. Math., 32 (1975), no. 2, 291-300.
Z227.12004; M52#3113; R1976,3A137

[20] On representations of numbers by sums of squares and quadratic field, Arch. Math. (Brno), 13 (1977), no. 1, 29-40.
Z275.10031; M57#5932; R1978,4A115

[21] On the class number of divisors of a real quadratic field, II, Modern Algebra, pp. 124-128, Leningrad. Gos. Ped. Inst., Leningrad, 1980.
Z482,12006; 583.12006; M82b:12003; R1980,10A284

[22] A remark on the paper of T. Uehara "On p-adic continuous functions determined by the Euler numbers", these reports, No. 8 (1980), 1-8, Reports of the Faculty of Science and Engineering, Saga Univ., 15 (1987), no. 1, 1-2.
Z613.10013; M88c:11071; R1987,10A65

[23] Ob ekvivalentnosti sravnenij Voronogo i Vandivera [On the equivalence of Voronoi's and Vandiver's congruences]. Voprosy teoreticheskoj i prikladnoj matematiki. Leningrad, 1986, 80-86.
R1986,11A65

[24] p-adic continuous Uehara functions and Voronoi's congruence. Engl. Transl. in: Soviet Math. (Izv. VUZ), 31 (1987), no. 4, 79-85.
Z632.10007; M88k:11019; R1987,9A131

[25] A remark on the note of Gh. Stoica: "A recurrence formula in the theory of the Riemann zeta function", Stud. Cerc. Mat., 41 (1989), no. 4, 333.
Z681.10007; M91b:11089

[26] Shtaudt i chisla Bernulli [Staudt and Bernoulli numbers]. Conference Report of the 9th Czechoslovak Colloquium on Number Theory held at Rackova Dolina, Sept. 1989. pp. 92--96. Masaryk Univ., Brno, 1990.
Z697.10038

[27] Outline of the history of research on the arithmetic properties of Bernoulli numbers. Staudt, Kummer, Voronoi. (Russian) Istor.-Mat. Issled., no. 32-33 (1990), 158-181.
Z734.01008; M92m:11001

[28] A note on Bernoulli numbers. J. Number Theory, 53 (1995), no. 2, 309-310.
Z830.11009; M96f:11031

[29] Staudt and arithmetical properties of Bernoulli numbers, Historia Sci. (2), 5 (1995), no. 1, 69-74.
Z864.11003; M96j:11005

[30] About von Staudt congruences for Bernoulli numbers, Comment. Math. Univ. St. Paul. 48 (1999), no. 2, 137-144.

[31] Leudesdorf's theorem and Bernoulli numbers, Arch. Math. (Brno) 35 (1999), 299-303.

SLAVUTSKII I.SH.: see also CLARKE F., SLAVUTSKII I.SH.

SLAVUTSKII I.SH.: see also KISELEV A.A., SLAVUTSKII I.SH.

SLAVUTSKII I.SH.: see also SKULA L., SLAVUTSKII I.SH.

SLAVUTSKII I.SH.: see also DILCHER K., SKULA L., SLAVUTSKII I.SH.

SLOANE N.J.A.,
[1] A handbook of integer sequences, Academic Press, New York-London, 1973. xiii + 206 pp.
Z286.10001; M50#9760; R1975,1V488K

SLOANE N.J.A., PLOUFFE S.,
[1] The encyclopedia of integer sequences. Academic Press, Inc., San Diego, CA, 1995. xiv+587pp.
Z845.11001; M96a:11001

SLOANE N.J.A.: see also BERNSTEIN M., SLOANE N.J.A.

SLOANE N.J.A.: see also CONWAY J.H., SLOANE N.J.A.

SLOANE N.J.A.: see also MILLAR J., SLOANE N.J.A., YOUNG N.E.

SMALL D.: see IRELAND K., SMALL D.

SMITH D.E.,
[1] A Source Book in Mathematics, Dover Publications, Inc., New York, 1959.
J55,583; Z86,2; M21#4873

SMITH H.J.S.,
[1] Report on the theory of numbers, Report of the British Association for 1860, The collected math. papers, 93-162, Oxford: Clarendon Press, vol.1, 1894, xcv + 603pp.
J25.29

SMORYNSKI C.,
[1] Logical Number Theory I. An Introduction. Springer Verlag, Berlin, etc., 1991, x+405 pp.
Z759.03002; M92g:03001

SNOW D.R.,
[1] Formulas for the sums of powers of integers by functional equations. Aequationes Math., 18 (1978), no. 3, 269-285.
Z398.05010; M80a:10005; R1979,9A102

SNYDER C.,
[1] Partial fraction decompositions and Kummer congruences for the normalized coefficients of the Laurent expansion of elliptic functions parametrizing a nonsingular cubic curve in Hessian normal form, J. Reine Angew. Math., 306 (1979), 60-87.
Z398.12005; M80d:10036; R1979,10A314

[2] A concept of Bernoulli numbers in algebraic function fields, J. Reine Angew. Math., 307/308 (1979), 295-308.
Z398.12006; M81a:12016; R1980,1A377

[3] A concept of Bernoulli numbers in algebraic function fields, II, Manuscripta Math., 35 (1981), no. 1/2, 69-89.
Z478.12013; M83e:12009; R1982,4A373

[4] Kummer congruences in formal groups and algebraic groups of dimension one, Rocky Mountain J. Math., 15 (1985), no. 1, 1-11.
Z578.14041; M86j:14044

[5] p-adic interpolation of Dedekind sums, Bull. Austral. Math. Soc., 39 (1988), no. 2, 293-301.
Z632.10023; M89b:11039; R1988,10A123

SNYDER C.: see also ÖZLÜK A.E., SNYDER C.

SNYDER C.: see also KALLIES J., SNYDER C.

SNYDER W.M.: see ROSEN K.H., SNYDER W.M.

SOLOMON D.,
[1] On the classgroups of imaginary abelian fields, Ann. Inst. Fourier, 40 (1990), no. 3, 467-492.
Z659.00011;694.12004; M92a:11133; R1991,10A209

SOLOVJEV A.A.: see PETROVA S.S., SOLOVJEV A.A.

SOMASUNDARAM D.,
[1] A formula of Srinivasa Ramanujan in Notebook 3, Math. Student, 59 (1991), no. 1-4, 161-64.
Z781.33001; M93c:11011

SOMPOLSKI R.W.: see BUHLER J.P., CRANDALL R.E., SOMPOLSKI R.W.

SONDOW J.,
[1] Analytic continuation of Riemann's zeta function and values at negative integers via Euler's transformation of series. Proc. Amer. Math. Soc., 120 (1994), no. 2, 421-424.
Z796.11033; M94d:11066; R1994,8A144

SONIN N.YA.,
[1] O bernullievykh polinomakh i ikh prilozheniyakh [On Bernoullian polynomials and their applications]. Izv. Varshavsk. Universiteta, (1888), no. 3-4, 1-48.
J20.427

[2] O preryvnoj fynktsii $[x]$ i ee prilozheniyakh [On the discontinuous function $[x]$ and its applications]. Izv. Varshavsk. Universiteta, (1889), no. 7-8, 1-78.
J21.444

[3] Sur les termes complémentaires de la formule sommatoire d'Euler et de celle de Stirling, Ann. Sci. École Norm. Supér. (3), 6 (1889), 257-262.
J21.235

[4] Sur les termes complémentaires de la formule sommatoire d'Euler et de celle de Stirling, C.R. Acad. Sci. Paris, 108 (1889), 725-727.

[5] Ryad Ivana Bernulli. (Epizod iz istorii matematiki) [The series of Jean Bernoulli. (An episode from the history of mathematics)]. Bull. St. Petersb. Acad. Sci., 7 (1895), 337-353.
J1895,275-276

SONIN N.YA., HERMITE CH.,
[1] Sur les polynômes de Bernoulli, J. Reine Angew. Math, 116 (1896), 133-156.
J21.209

SOULÉ CH.,
[1] K-théorie et corps cyclotomique. Séminaire de théorie des nombres, Univ. Bordeaux I, année 1980-81, 1981, exp. no.15, 6 pp.
Z495.12009; M82m:10006

[2] Perfect forms and the Vandiver conjecture, J. Reine Angew. Math. 517 (1999), 209-221.

SPIEGEL M.G.,
[1] Theory and problems of calculus of finite differences and difference equations, Schaum Outlines, New York, 1971.
Z243.39001

SPIESS J.,
[1] Some identities involving harmonic numbers, Math. Comp., 55 (1990), no. 192, 839-863.
Z724.05005; M91c:05021

SPIRA R.,
[1] The nonvanishing of the Bernoulli polynomials in the critical strip, Proc. Amer. Math. Soc., 17 (1966), 1476-1477.
Z154,319; M34#2967; R1967,10V247

SPITZER S.,
[1] Note über die Summenformel $\sum x^m$, Arch. für Math. und Phys., 23 (1854), 457-460.

SQUIRE W.: see GOULD H.W., SQUIRE W.

SRINIVASAN S.,
[1] A footnote to a conjecture in number theory, Rend. Accad. Naz. Sci. XL Mem. Mat. (5), 10 (1986), no. 1, 39-42.
Z632.10042; M88m:11077; R1987,7A103

SRIVASTAVA H.M.,
[1] Some explicit formulas for the Bernoulli and Euler numbers and polynomials, Internat. J. Math. Ed. Sci. Tech., 19 (1988), no. 1, 79-82.
Z(608.10016)628.10010; M89c:11035

SRIVASTAVA H.M., JOSHI J.M.C., BISHT C.S.,
[1] Functional Calculus and the sums of powers of natural numbers. Stud. Appl. Math., 85 (1991), no. 2, 183-193.
Z727.11008; M92g:11022

SRIVASTAVA H.M., TODOROV P.G.,
[1] A short proof of the Srivastava-Todorov formula for the generalized Bernoulli polynomials, Plovdiv. Univ. Nauchn Trud., 26 (1988), no. 3, 25-30.
Z732.11012

[2] An explicit formula for the generalized Bernoulli polynomials, J. Math. Anal. Appl., 130 (1988), 509-513.
Z621.33008; M89d:33021; R1988,8B13

SRIVASTAVA H.M.: see also CHEN MING-PO, SRIVASTAVA H.M.

STACHEFF J.: see MILNOR J.W., STACHEFF J.

STAFFORD E.T., VANDIVER H.S.,
[1] Determination of some properly irregular cyclotomic fields, Proc. Nat. Acad. Sci. USA, 16 (1930), 136-150.
J56.887

STARK E.L.,
[1] A new method of evaluating the sums of $\sum_{k=1}^\infty (-1)^{k+1} k^{-2p}$, $p=1,2,3,\ldots$ and related series. Elem. Math., 27 (1972), 32-34.
Z225.40002; M45#3996; R1972,8B26

[2] The series $\sum_{k=1}^\infty k^{-s}$, $s=2,3,4,\ldots$, once more, Math. Mag., 47 (1974), no. 4, 197-202.
Z291.40004; M50#5261; R1975,5B17

STARK H.M.,
[1] Values of zeta and L-functions, Abhandl. Braunsch. Wiss. Gesellsch., 33 (1982), 71-83.
Z509.12012; M85c:11110; R1983,5A102

[2] Modular forms and related objects. Number theory (Montreal, 1985), pp. 421-455, CMS Conf. Proc., 7, Amer. Math. Soc., Providence, R.I., 1987.
Z624.10013; M88j:11029

[3] Dirichlet's class-number formula revisited. A tribute to Emil Grosswald: number theory and related analysis, 571--577, Contemp. Math., 143, Amer. Math. Soc., Providence, RI, 1993.
Z804.11060; M94a:11133; R1994,2A341

STATE E.Y.,
[1] A one-sided summatory function. Proc. Amer. Math. Soc., 60 (1976), 134-138.
Z348.40001; M54#10615; R1976/77,9B101

STAUDT K.G.C. von,
[1] Beweis eines Lehrsatzes die Bernoulli'schen Zahlen betreffend, J. Reine Angew. Math., 21 (1840), 372-374.

[2] De Numeris Bernoullianis, Erlangen, 1, 2, Adolf Ernst June, Erlangen, 1845.

STEFANI W.,
[1] Über eine Klasse von Polynomen und ihre Beziehungen zu den Bernoullischen Zahlen, Math. Nachr., 29 (1965), 131-149.
Z131,41; M32#2371; R1966,10A94

[2] Über eine Klasse von Polynomen und ihre Beziehungen zu den Bernoullischen Zahlen, II, Math. Nachr., 36 (1968), 15-37.
Z162,58; M37#3997; R1969,12V378

STEFFENSEN J.F.,
[1] Interpolation, 2nd ed., Chelsea Publ. Co., New York, 1950, ix + 248 pp.
Z41,026; M12-164d

[2] On a generalization of Nörlund's polynomials. Kgl. Danske Vidensk. Selsk. Mat.-fys. Meddelser, 7 (1926), no. 5, 18p.
J52.467

STEGUN I.A.: see ABRAMOWITZ M., STEGUN I.A.

STEIN P.R.: see RIORDAN J., STEIN P.R.

STEKLOV W.,
[1] Remarques relatives aux formules sommatoires d'Euler et de Boole, Soobshch. Kharkovsk. mat. obshchestva, 2, 8 (1902), 136-195.
J35.263

STEPHENS A.J., WILLIAMS H.C.,
[1] Some computational results on a problem concerning powerful numbers, Math. Comp., 50 (1988), no. 182, 619-632.
Z642.12001; M89d:11091; R1989,1A292

STERN M.A.,
[1] Über die Coefficienten der Secantenreihe, J. Reine Angew. Math., 26 (1843), 88-91.

[2] Zur Theorie der Eulerschen Zahlen, J. Reine Angew. Math., 79 (1875), 67-98.
J6.103

[3] Über eine Eigenschaft der Bernoulli'schen Zahlen, J. Reine Angew. Math., 81 (1876), 290-294.
J8.146

[4] Zur Theorie der Bernoullischen Zahlen. Auszug aus einem Schreiben an Herrn Borchardt. J. Reine Angew. Math., 84 (1878), 267-269.
J9.185

[5] Beiträge zur Theorie der Bernoullischen und Eulerschen Zahlen, Abhandl. Gesellsch. Wiss. Göttingen, Math., 23 (1878), 1-44.

[6] Zur Theorie der Bernoullischen Zahlen, J. Reine Angew. Math., 88 (1880), 85-95.
J11.186

[7] Beiträge zur Theorie der Bernoullischen und Eulerschen Zahlen, Abhandl. Gesellsch. Wiss. Göttingen, Math., 26 (1880), 1-45.

[8] Zur Theorie der Bernoullischen Zahlen, J. Reine Angew. Math., 92 (1882), 349-350.
J14.191

[9] Sur une propertiété des nombres de Bernoulli, Bull. Soc. Math. France, 10 (1886), 280-282.
J18.225

STEVENS G.,
[1] Arithmetic on modular curves, Progress in Math., 20. Birkhäuser Boston, Inc., Boston, Mass., 1982, xvii + 214pp.
Z529.10028; M87b:11050

[2] The cuspidal group and special values of L-functions, Trans. Amer. Math. Soc., 291 (1985), no. 2, 519-550.
Z579.10011; M87a:11056; R1986,6A673

[3] Stickelberger elements and modular parametrizations of elliptic curves, Invent. Math., 98 (1989), no. 1, 75-106.
Z697.14023; M90m:11089; R1990,3A393

STEVENS G.: see also KAMIENNY S., STEVENS G.

STEVENS H.,
[1] Generalized Kummer congruences for products of sequences, Duke Math. J., 28 (1961), 25-38.
Z122,46; M23#A849; R1962,2A142

[2] Generalized Kummer congruences for the products of sequences. Applications. Duke Math. J., 28 (1961), 261-275.
Z122,47; M23#A850; R1962,2A135

[3] Kummer's congruences of a second kind, Math. Z., 79 (1962), 180-182.
Z106,32; M29#5809; R1963,2A135

[4] Kummer congruences for products of numbers, Math. Nachr., 24 (1962), no. 4, 219-227.
Z106,32; M27#1407; R1963,6A133

[5] Bernoulli numbers and Kummer's criterion, Fibonacci Quart., 24 (1986), no. 2, 154-158.
Z588.10012; M87f:11017; R1986,12A161

STEVENS H.: see also CARLITZ L., STEVENS H.

STEWART D.: see ISMAIL M.E.H., STEWART D.

STEWART I.N., TALL D.O.,
[1] Algebraic number theory, Chapman and Hall, London, 1979, xviii + 257 pp.
Z413.12001; M81g:12001; R1980,11A121K

STHAPIT R.K.,
[1] The Bernoulli Numbers and Polynomials, M.Sc. thesis, Southern Illinois University, Carbondale, 1982.

STIEIRMAN I.JA., AKHIEZER N.I.,
[1] Über den Zusammenhang zwischen der Störmerschen Integrationsmethode und den Bernoullischen Polynomen, Zap. fiz. otdeleniya Akad. Nauk Ukr. SSR, 2 (1927), N 2, 16-24.
J53.342,414

STÖCKLER J.,
[1] Multivariate Bernoulli splines and the periodic interpolation problem, Constr. Approx., 7 (1991), no. 1, 105-122.
Z721.41015; M91j:41013; R1991,10B118

[2] Interpolation mit mehrdimensionalen Bernoulli- Splines und periodischen Box-Splines. Dissertation, Univ. (Gesamthochschule) Duisburg, Fachbereich Mathematik, 141 pp., 1988.
Z718.41010

[3] On minimum norm interpolation by multivariate Bernoulli splines. Approximation Theory VI, Proc. 6th Int. Symp., College Station, TX. 1989, Vol. II, 635-638 (1989).
Z727.41011; M91j:41002

STOICA G.,
[1] A recurrence formula in the study of the Riemann zeta function (Romanian. English summary). Stud. Cerc. Mat., 39 (1987), no. 3, 261-264.
Z633.10036; M88i:11060; R1988,2A113

[2] On Riemann's zeta function, An. Univ. Bucuresti Mat., 37 (1988), no. 1, 60-64.
Z651.10025; M90a:11103

[3] Some remarks concerning Riemann's zeta function, Stud. Cerc. Mat., 40 (1988), no. 5, 447-454.
Z659.10046; M89m:30061; R1989.5A68

STRAUCH O.,
[1] Some applications of Franel's integral. I. Acta Math. Univ. Comenian., 50/51 (1987), 237-246 (1988).
Z667.10023; M90d:11028; R1989,10A136

[2] Some applications of Franel-Kluyver's integral. II. Math. Slovaca, 39 (1989), no. 2, 127-140.
Z671.10002; M90j:11079; R1989,9A103

STRAUSS H.,
[1] Optimal quadrature formulas, Approximation in Theorie und Praxis (Proc. Symp., Siegen, 1979), 239-250, Bibliographisches Inst., Mannheim, 1979.
Z436.41015; M81b:41024

[2] Optimale Quadraturformeln und Perfektsplines, J. Approx. Theory, 27 (1979), no. 3, 203-226.
Z427.41017; M80m:41007; R1980,7B32

STREHL V.,
[1] Alternating permutations and modified Gandhi polynomials, Discrete Math., 28 (1979), 89-100.
Z426.05005; M81d:05008; R1980,3V605

STREHL V.: see FOATA D., STREHL V.

STRICHARTZ R.S.,
[1] Estimates for sums of eigenvalues for domains in homogeneous spaces, J. Funct. Anal. 137 (1996), no. 1, 152-190.
Z848.58050; M97g:58172

STUDNICKA F.J.,
[1] O novem neodvislem vyjadreni cisel Bernujskich a o vlastnotech prislusneho determinantu [On a new independent representation of the Bernoulli numbers and on properties of related determinants], (Czech), Casopis Pest. Mat. a Fyz., 15 (1886), 97-102.
J18.224

[2] Ueber ein Analogon der Euler'schen Zahlen. Sitzungsber der Kgl. Böhmischen Ges. der Wiss., Prag, 1900, no. 9, 8p.
J31.438

[3] Ueber neue Fermat'sche Lehrsätze. Casopis Pest. Mat. a Fyz., 29 (1900), 257-261.
J31.438

STÜNZI M.: see GUT M., STÜNZI M.

SUBRAMANIAN P.R.,
[1] A short note on the Bernoulli polynomial of the first kind, Math. Student, 42 (1974), 57-59, (1975).
Z358.10005; M53#817; R1977,2V431

[2] Evaluation of ${\rm Tr}(J\sp {2p}\sb \lambda)$ using the Brillouin function, J. Phys. A, 19 (1986), no. 7, 1179-1187.
Z614.33021; M87i:82082

[3] Generating functions for angular momentum traces, J. Phys. A, 19 (1986), no. 13, 2667-2670.
Z614.33022; M87k:81037

SUBRAMANIAN P.R., DEVANATHAN V.,
[1] Generation of angular momentum traces and Euler polynomials by recurrence relations, J. Phys. A, 18 (1985), no. 15, 2909-2915.
M87b:81060; R1985,7V581

[2] Recurrence relations for angular momentum traces, J. Phys. A, 13 (1980), 2689-2693.

SUN ZHI-HONG,
[1] A supplement to a binomial inversion formula. (Chinese) Nanjing Daxue Xuebao Shuxue Bannian Kan 12 (1995), no. 2, 264-271.
Z871.11012; M97d:05009; R1997,12V234

[2] Congruences for Bernoulli numbers and Bernoulli polynomials. Discrete Math. 163 (1997), no. 1-3, 153--163.

Z872.11012; M98b:05001

SUN ZHI-WEI: see GRANVILLE A., SUN ZHI-WEI

SUNCERI R.F.,
[1] Zeros of p-adic L-functions and densities relating to Bernoulli numbers, Ph.D. Thesis, Univ. of Illinois at Urbana-Champaign, 1979.

SUNDARAM S.,
[1] Plethysm, partitions with an even number of blocks and Euler numbers. Formal power series and algebraic combinatorics (New Brunswick, NJ, 1994), 171--198, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 24, Amer. Math. Soc., Providence, RI, 1996.
Z845.05100; M97c:05162

SURY B.,
[1] The value of Bernoulli polynomials at rational numbers. Bull. London Math. Soc., 25 (1993), no. 4, 327-329.
Z807.11014; M94g:11018; R1995,3A64

SUTTON J.R.,
[1] A series related to Bernoulli's numbers, Nature, 66 (1902), 492.
J33.291

SWINNERTON-DYER H.P.F.,
[1] On $l$-adic representations and congruences for coefficients of modular forms. In: Modular functions of one variable, III (Proc. Int. Summer School, Univ. Antwerp, 1972), pp. 1-55. Lecture Notes in Math., Vol. 350, Springer-Verlag, Berlin, 1973.
Z267.10032; M53#10717a; R1974,6A443

SYLVESTER J.J.,
[1] Note on the numbers of Bernoulli and Euler, and a new theorem concerning prime numbers, Phil. Magaz., 21 (1861), 127-136.

[2] Sur une properiété de nombres premiers qui se rattache au dernier théorème de Fermat, C.R. Acad. Sci., Paris, 52 (1861), 161-163.

[3] Addition à la précédente note, C.R. Acad. Sci., Paris, 52 (1861), 212-214.

[4] Note relative aux communications faites dans les séances des 28 Janvier et 4 Fèvrier 1861, C.R. Acad. Sci., Paris, 52 (1861), 307-308.

SZÁSZ O.,
[1] Über die Approximation stetiger Funktionen durch Bernoullische Polynome, J. Reine Angew. Math., 148 (1918), 183-188.

SZEGÖ G.: see POLYA G., SZEGÖ G.

SZENES, A.,
[1] Iterated residues and multiple Bernoulli polynomials, Internat. Math. Res. Notices 1998, no. 18, 937-956.
Z990.19296

SZMIDT J., URBANOWICZ J.,
[1] Some new congruences for generalized Bernoulli numbers of higher orders, preprint, 30pp.

SZMIDT J., URBANOWICZ J., ZAGIER D.,
[1] Congruences among generalized Bernoulli numbers. Acta Arith., 71 (1995), no. 3, 273-278.
Z829.11011; M96f:11032; R1996,4A75


TAKÁCS L.,
[1] On generalized Dedekind sums. J. Number Theory, 11 (1979), no. 2, 264-272.
Z404.10006; M80j:10019; R1979,12A107

TAKAGI T.,
[1] On the law of recipricity in the cyclotomic corpus, Proc. Phys.-Math. Soc. Japan (3), 4 (1922), 173-182.
J48.169

[2] Cuspidal class number formula for the modular curves $X_1(p)$. J. Algebra, 151 (1992), no. 2, 348-374.
Z773.11040; M93g:11063

[3] The cuspidal class number formula for the modular curves $X_1(p^m)$. J. Algebra, 158 (1993), no. 2, 515-549.
M94d:11040

TALBOT R.F.: see BURROWS B.L., TALBOT R.F.

TALL D.O.: see STEWART I.N., TALL D.O.

TAMARKINE J.: see FRIEDMANN A.A., TAMARKINE J.

TAMBS LYCHE R.,
[1] Sur les coefficients du développement de $1/\cos x$ en série entière. Bull. Sci. Math. (2), 50 (1926), 230-236.
J52.356

[2] Bemerkung zu den Formeln von I. J. Schwatt für die Eulerschen Zahlen. Math. Z., 32 (1930), 586.
J56.II.872

[3] Tillegg til foranstående artikkel (supplement to the previous paper), Nordisk Mat. Tidsskrift, 6 (1958), 159-161, 182.
Z088.02003

TAMME G.,
[1] Über die p-Klassengruppe des p-ten Kreisteilungskörpers, Ber. Math.-Stat. Sekt. Forschungsgesellsch. Joanneum, 1988, no. 299, 1-48.
Z653.12002; M91b:11117; R1988,12A313

TANEJA V.S.: see GANDHI J.M., TANEJA V.S.

TANNER J.W.,
[1] Proving Fermat's last theorem for many exponents by computer. B.A. Thesis, Harvard Univ., 1985.

TANNER J.W., WAGSTAFF S.S., JR.,
[1] New bound for the first case of Fermat's last theorem, Math. Comp., 53 (1989), no. 188, 743-750.
Z694.10018; M90h:11028

TANNER J.W.: see also WAGSTAFF S.S., JR., TANNER J.W.

TANNERY P.,
[1] Introduction à la théorie des fonctions d'une variable, Paris, 1886, Ch. 7.
J18.328

TANTURRI A.,
[1] Dalla formola di Pascal a quella di Bernoulli sulle somme delle potenze simili dei primi $n$ numeri. Periodico di Mat. (3), 5 (1907), 80-83.
J38.314

[2] Un expressione nuova dei numeri Bernoulliani. Rom. Acc. L. Rend. (5), 30 (1921), 44-46.
J48.1194

TAO QING SHENG,
[1] Generalizations of Bernoulli polynomials and Euler-Maclaurin formulas (Chinese. English summary). Gaoxiao Yingyong Shuxue Xuebao, 7 (1992), no. 2, 177-183.
Z778.11013

TASCHNER R.: see HLAWKA E., SCHOISSENGEIER J., TASCHNER R.

TAUBER S.,
[1] Combinatorial numbers in ${\bf C}^n$, Fibonacci Quart. 14 (1976), no. 2, 101-110.
Z352.05005; M53#7795; R1977,3V374

TAUSSKI O., TODD J.,
[1] Some discrete variable computations, Proc. Symp. Appl. Math., 10 (1960), 201-209.
Z96,5; M22#6063; R1961,9A136

TAYLOR B.D.: see ROTA G.-C., TAYLOR B.D.

TAYLOR M.J.: see CASSOU-NOGUÈS PH., TAYLOR M.J.

TCHISTIAKOV I.I.: see CHISTYAKOV I.I.

TEIXEIRA F.G.,
[1] Note sur les nombres de Bernoulli, Amer. J. Math., 7 (1885), 288-292.
J17.231

[2] Sur les démonstrations de deux formules pour le calcul des nombres de Bernoulli, Enseign. Math., 7 (1905), 442-446.
J36.412

TEIXEIRA J.P.,
[1] Sur les nombres Bernoulliens, J. Sci. Math., Lisboa, 3 (1893) (1895), 73-75.
J26.412

TEMME N.M.,
[1] Bernoulli polynomials old and new: Problems in complex analysis and asymptotics. Apt, Krzysztof (ed.) et al., From universal morphisms to megabytes: a Baayen space Odyssey. On the occasion of the retirement of Prof. Dr. P. C. Baayen. Amsterdam: CWI, 559-576 (1994).
Z879.11008; M99a:11020

[2] Bernoulli polynomials old and new: generalizations and asymptotics, CWI Quarterly, 8 (1995), no. 1, 47-67.
Z879.11008; M96j:11020

[3] Special Functions. An Introduction to the Classical Functions of Mathematical Physics, John Wiley & Sons, New York, etc., 1996.
Z856.33001; M97e:33002

TEMME N.M.: see also LÓPEZ J.L.; TEMME N.M.

TEPPER M.,
[1] Combinations and sums of powers, Fibonacci Quart. 12 (1974), 196-198.
Z281.10005; M50#4472

TERRILL H.M.,
[1] Methods for computing generalized Euler numbers, Amer. Math. Monthly, 44 (1937), 526-527.
Z17,204

TERRILL H.M., TERRILL E.M.,
[1] Tables of numbers related to the tangent coefficients, J. Franklin Institute, 239 (1945), 66-67.

TERRY T.R.,
[1] Question 9141, Math. questions and solutions from the "Educat. Times", London, 10 (1906), 70.
J37.297

THACKER A.,
[1] Ein Beitrag zur Zahlentheorie, J. Reine Angew. Math., 40 (1850), 89-92.

[2] Propositions in the theory of numbers, Camb. and Dubl. Math. J., 5 (1850), 243-248.

THAINE F.,
[1] Polinômios que generalizam os coeficientes binomiais e sua aplicaçáo no estudo do último theorema de Fermat, Ph.D. thesis, Rio de Janeiro, 1979, 86 pp.

[2] Polynomials generalizing binomial coefficients and their application to the study of Fermat's last theorem, Fundação Universidade de Brasília, Trabalho de Matemática, No. 156, Nov. 1979, 1-70.

[3] Polynomials that generalize binomial coefficients and their applications to Fermat's last theorem. (Portuguese). Proc. Twelfth Brazilian Math. Coll., Vol. I, II (Poços de Caldas, 1979), pp.50-64, Rio de Janeiro, 1981.
Z504.10009; M84j:10013

[4] Polynomials generalizing binomial coefficients and their application to the study of Fermat's last theorem, J. Number Theory, 15 (1982), no. 3, 304-317.
Z504.10009; M84d:10023; R1983,8A137

[5] On the first case of Fermat's last theorem, J. Number Theory, 20 (1985), no. 2, 128-142.
Z571.10016; M87d:11021; R1986,2A131

[6] On the ideal class groups of real abelian number fields, Universidade Estadual de Campinas, Sao Paolo, Brasil, Relatorio Interno, No. 355, Jun. 1986, 1-37.

[7] On Fermat's last theorem and the arithmetic of $ Z[\xi_p + \xi_p^{-1}]$, Relatório Técnico, Instituto de Matemática, Universidade Estadual de Campinas, Campinas - Sao Paolo, Brasil, No. 22/87, Jun. 1987, 1-6.

[8] On the ideal class groups of real abelian number fields, Ann. of Math. (2), 128 (1988), no. 1, 1-18.
Z665.12003; M89m:11099; R1989,4A259

[9] On Fermat's last theorem and arithmetic of $ Z[{\zeta}_p + {{\zeta}_p}^{-1}]$, J. Number Theory, 29 (1988), no. 3, 297-299.
Z654.10018; M89m:11029; R1989,1A106

[10] On the relation between units and Jacobi sums in the prime cyclotomic fields. Manuscripta Math., 73 (1991), no. 2, 127-151.
Z760.11030; M92m:11122; R1992,4A298

[11] On the $p$-part of the ideal class group of ${\openQ}(\zeta_p + \zeta^{-1}_p)$ and Vandiver's conjecture. Michigan Math. J., 42 (1995), no. 2, 311-344.
Z844.11069; M96e:11140

THAKARE N.K.,
[1] Generalization of Bernoulli, Euler numbers and related polynomials, Boll. Un. Mat. Ital. B (5), 18 (1981), no. 3, 847-857.
Z475.33010; M83m:05009; R1982,5B55

THAKARE N.K.: see also KARANDE B.K., THAKARE N.K.

THAKUR D.S.,
[1] Zeta measure associated to $F_q[T]$, J. Number Theory, 35 (1990), no. 1, 1-17.
Z703.11065; M91e:11139

THANG LE THU QUAC, MURAKAMI JUN,
[1] On Kontsevich's integral for the Homfly polynomial and relations of fixed Euler numbers. Max-Planck-Institut für Math., Bonn, MPI/93-26, 17 pp.

THIRUVENKATACHARYA V.,
[1] Some properties of Euler's numbers and associated polynomials. J. Indian Math. Soc., 16 (1927), Suppl., 19.
J(52.361)

THOMAN F.,
[1] Logarithmes des 40 premiers nombres de Bernoulli, C.R. Acad. Sci., Paris, 50 (1860), 905-906.

[2] Développement des séries à termes alternativement positifs et negatifs à l'aide des nombres de Bernoulli, C.R. Acad. Sci., Paris, 64 (1867), 655-659.

THOMAS C.B.,
[1] Cohomology of metacyclic groups and class numbers of subfields of cyclotomic extensions, J. Algebra, 164 (1994), no. 1, 53-84.

Z816.11056; 95k:11153

TIJDEMAN R.: see GYÖRY K., TIJDEMAN R., VOORHOEVE M.

TITCHMARSH E.C.,
[1] The theory of the Riemann zeta-function, Oxford, Clarendon Press, 1951, vi+346pp. (2nd Ed., 1986, M88c:1049.)
Z42.79; M13-741c

TITS L.,
[1] Identités nouvelles pour le calcul des nombres de Bernoulli. Nouv. Ann. Math. (5), 1 (1923), 191-196.
J49.167

TODD J.: see TAUSSKI O., TODD J.

TODOROV P.G.,
[1] Une nouvelle représentation explicite des nombres d'Euler, C.R. Acad. Sci., Paris, 286A (1978), no. 19, 807-809.
Z378.10007; M58#27737; R1978,11A89

[2] On a new explicit representation of Euler numbers, Plovdiv Univ. Nauchn.Trud., 16 (1978), no. 1, 259-301 (1980).
M82m:05006

[3] The nth derivative of $tg z$, Plovdiv Univ. Nauchn. Trud., 21 (1983), no. 1, 93-98.
Z599.30042

[4] On the theory of the Bernoulli polynomials and numbers, J. Math. Anal. Appl., 104 (1984), no. 2, 309-350.
Z552.10007; M86h:05020; R1986,1B22

[5] Une formule simple explicite des nombres de Bernoulli généralisés, C.R. Acad. Sci. Paris, Sér. A, 301 (1985), no.13, 665-666.
Z606.10008; M87e:11025

[6] Taylor expansions of certain composite functions, C.R. Acad. Bulgare Sci., 39 (1986), no. 11, 15-18.
Z624.05003; M88b:05009; R1987,6B3

[7] The nth derivative of $tg z$. Functiones et Approximatio, Adam Mickiewicz University Press, Poznán, XV (1986), 171-173.
Z621.33003

[8] On certain formulas for the Stirling numbers of the first and the second kind, Plovdiv. Univ. Nauchn. Trud., 26 (1988), no. 3, 17-23.
Z735.11013

[9] Taylor expansions of analytic functions related to $(1 + z)^x - 1$, J. Math. Anal. Appl., 132 (1988), no. 1, 264-280.
Z646.30002; M89e:30001; R1988,10B148

[10] Recurrence relations for certain polynomials, Facta Univ. Ser. Math. Inform., 4 (1989), 19-26.
Z702.11008; M91g:11019

[11] On certain formulas for the Stirling numbers of the first and the second kind, Punjab Univ. J. Math., 22 (1989-90), 31-35.
Z723.11013; M91f:11011

[12] A disproof of a conjecture of Robertson, Mitt. Math. Ges. Hamburg, 12 (1991), no.2, 495-497.
Z780.30003; M93a:30029

[13] Explicit formulas for the Bernoulli and Euler polynomials and numbers. Abh. Math. Sem. Univ. Hamburg, 61 (1991), 175-180.
Z748.11016; M93b:11019

[14] A disproof of a conjecture of Robertson and generalizations. Punjab Univ. J. Math. (Lahore), 23 (1990), 83-91.
Z734.30019; M92k:30003

[15] A disproof of a conjecture of Robertson and generalizations. Publ. Inst. Mathématique (Beograd) (N.S.) 50, 64 (1991),105-110.
Z780.30002; M94k:30003

[16] Explicit and recurrence formulas for generalized Euler numbers. Funct. Approx. Comment. Math., 22 (1993), 13-17 (1994).
Z827.11011; M95h:11016

[17] Partial fraction decomposition and a new form of the Taylor expansion of the function $(z/(e^z-1))^m$. Funct. Approx. Comment. Math., 23 (1994), 59-67 (1995).
Z873.41030; M96e:11028; R1996,8B252

TODOROV P.G.: see also SRIVASTAVA H.M., TODOROV P.G.

TOLSTIKOV A.V.,
[1] Application of fields generated by Gauss periods to the study of cyclic Diophantine equations. Studies in number theory. 4. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 67 (1977), 201-222, 227.
Z368.10015; M56#2913; R1977,7A159

[2] Application of fields generated by Gauss periods to the study of cyclic Diophantine equations. II. Studies in number theory. 5. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 82 (1979), 149-157.
Z433.10008; M80h:10024; R1979,10A97

TOOLE B.A.: see KIM E.E., TOOLE B.A.

TORNHEIM L.,
[1] Harmonic double series. Amer. J. Math., 72 (1950), 303-314.
Z36.172; M11-654a

TOSCANO L.,
[1] Successioni ricorrenti e polinomi di Bernoulli e di Eulero, Accad. Sci. Fis. e Mat. Napoli, Rend., IV.S., 6 (1936), 55-61.
J62.II.11223; Z15.250

[2] Sui coefficienti della tangente e sui numeri di Bernoulli, Boll. Un. Mat. Ital., 15 (1936), 8-12.
J62.I.50; Z13,198

[3] Polinomi e numeri di Bernoulli e di Eulero parametrizzati, Matematiche (Catania), 22 (1967), no. 1, 68-91.
Z154,65; M36#441; R1967,12V284

[4] L'operatore xD e i numeri di Bernoulli e di Eulero, Matematiche (Catania), 31 (1976), no. 1, 63-89 (1977). (English summary).
Z381.05001; M58#10709; R1978,11B50

[5] Some results for generalized Bernoulli, Euler, Stirling numbers, Fibonacci Quart., 16 (1978), no. 2, 103-112.
Z377.10009; M58#5257; R1978,11V633

[6] Recurring sequences and Bernoulli-Euler polynomials, J. Comb. Inform. System Sci., 4 (1979), no. 4, 303-308.
Z434.10011; M81e:10010; R1981,6V560

TOSCANO L.: see also ROSSI F.S., TOSCANO L.

TOUCHARD J.,
[1] Nombres exponentiels et nombres de Bernoulli, Canad. J. Math., 8 (1956), 305-320.
Z71,61; M18-16f; R1957,6835

[2] Sur les nombres et les polynômes de Bernoulli, Rend. del Circ. Mat. di Palermo, 50, 375-384.
J52.355;

TOYOIZUMI M.,
[1] Ramanujan's formulae for certain Dirichlet series, Comment. Math. Univ. St. Paul., 30 (1981), 149-173.
Z475.10033; M83c:10058

TRAKHTMAN YU. A.,
[1] The divisibility of certain differences that consist of binomial coefficients, (Russian). Akad. Nauk. Armjan. SSR Dokl., 59 (1974), no. 1, 10-16.
Z306.05003; M52#13613; R1975,5A109

[2] Divisibility of differences that consist of binomial coefficients, (Russian). Investigations in number theory, 131-137, Saratov. Gos. Univ., Saratov, 1987.
Z656.10008; M90m:11032; R1987,11A90

TRICOMI F.: see also ERDÉLYI A., MAGNUS W., OBERHETTINGER F., TRICOMI F.

TRUDI N.,
[1] Memoria sullo sviluppo di alcune funzioni trancendenti e sui numeri ultra-bernoulliani, Atti Inst. Incor. Sci. Natur. Napoli, 4 (1867), 105-131.

TSCHANTZ S.T.:see RATCLIFFE J.G., TSCHANTZ S.T.

TSUMURA H.,
[1] On a p-adic interpolation of the generalized Euler numbers and its applications, Tokyo J. Math., 10 (1987), no. 2, 281-293.
Z641.12007; M89k:11121; R1988,8A328

[2] On the values of a $q$-analogue of the $p$-adic $L$-function. Mem. Fac. Sci. Kyushu Univ. Ser. A, 44 (1990), no. 1, 49-60.
Z716.11060; M91b:11137

[3] A note on $q$-analogues of the Dirichlet series and $q$-Bernoulli numbers. J. Number Theory, 39 (1991), no. 3, 251-256.
Z735.11009; M92j:11020

[4] On a $q$-analogue of the log-$\Gamma$-function. Nagoya Math. J., 134 (1994), 57-64.
Z804.11018; M95g:33016

[5] On Demjanenko's matrix and Maillet's determinant for imaginary abelian number fields. J. Number Theory 60 (1996), no. 1, 70-79.
(See also METSÄNKYLÄ [17]: Letter to the editor.)
Z866.11063

TSVETKOV V.M.,
[1] $\Gamma$-extension and the co-restriction homomorphism. (Russian). Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 198 (1991), Voprosy Teor. Predstav. Algebr. Grupp. 2, 103-108, 113.
Z785.11053; M93e:11129; R1992,7A373

TUAN VU KIM; NGUYEN THI TINH,
[1] Expressions of Legendre polynomials through Bernoulli polynomials. Rev. Técn. Fac. Ingr. Univ. Zulia 18 (1995), no. 3, 285-290.
Z840.33003; M97f:33019

[2] Legendre, Euler and Bernoulli polynomials. C. R. Acad. Bulgare Sci. 49 (1996), no. 5, 19-21.
Z877.33004; M98d:33004

[3] Expressions of Legendre polynomials through Euler polynomials, Math. Balkanica (N.S.) 11 (1997), no. 3-4, 295-302.
M99i:33014

TYLER D.B.,
[1] Infinite integrals that are polynomials in $\pi^2$ (Problem E 3168; solution by C. Georghiou), Amer. Math. Monthly, 96 (1989), 58-59.


UEHARA T.,
[1] Vandiver's congruences for the relative class number of an imaginary abelian field, Mém. Fac. Sci. Kyushu Univ., Ser. A, 29 (1975), 249-254.
Z313.12006; M52#8087; R1976,3A140

[2] Bernoulli numbers in real quadratic fields (A remark on a work of H. Lang), Rep. Fac. Sci. Eng. Saga Univ., Math. 4 (1976), 1-5.
Z333.12006; M53#8017; R1976,11A195

[3] Fermat's conjecture and Bernoulli numbers, Rep. Fac. Sci. Eng. Saga Univ., Math., No. 6, (1978), 9-14.
Z379.10014; M80a:12008; R1978,12A179

[4] On p-adic continuous functions determined by the Euler numbers, Rep. Fac. Sci. Eng. Saga Univ., Math., No. 8, (1980), 1-8.
Z426.10015; M81e:12020; R1980,10A270; 1982,7A362

[5] On the Bernoulli numbers and the circular units of cyclotomic fields, Number Theory, Proc. Sympos., Koyoto, (1980), 47-60.

[6] On some congruences for generalized Bernoulli numbers, Rep. Fac. Sci. Eng. Saga Univ., Math., (1982), No. 10, 1-8.
Z493.12008; M83m:12014; R1982,10A306; 1983,2A57

[7] On cyclotomic units connected with p-adic characters, J. Math. Soc. Japan, 37 (1985), no. 1, 65-77.
Z547.12002; M87a:11110; R1985,8A399

[8] A certain congruence relation between Jacobi sums and cyclotomic units. Class numbers and fundamental units of algebraic number fields, Proc. Int. Conf. (Katata, 1986), pp. 33-52, Nagoya Univ., Nagoya, 1986.
Z615.o12006; M88m:11088

[9] On a congruence relation between Jacobi sums and cyclotomic units, J. Reine Angew. Math., 382 (1987), 199-214.
Z646.12002; M89a:11113; R1988,6A304

[10] On the first generalized Bernoulli number, Rep. Fac. Sci. Engrg. Saga Univ. Math., 24 (1995), no. 1, 11-21.
Z838.11017; M96j:11021; R1996,4A271

UENO K., NISHIZAWA M.,
[1] Multiple gamma functions and multiple $q$-gamma functions, Publ. Res. Inst. Math. Sci., 33 (1997), no. 5, 813-838.

UGRIN-SPARAC D.,
[1] Some number theoretic applications of certain polynomials related to Bernoulli polynomials (Romanian summary), An. Sti. Univ. "Al. I. Cuza" Iasi Sec. I a Mat. (N.S.), 14 (1968), 259-276.
Z199,364; M41#1664; R1970,2A86

[2] Lower bounds for sums of powers of different natural numbers expressed as functions of the sum of these numbers, J. Reine Angew. Math., 245 (1970), 74-80.
Z206,55; M43#3228; R1971,5A105

[3] One particular class of Eulerian numbers of higher order and some allied sequences of numbers, Publ. Math. Debrecen, 18 (1971), 23-35.
Z267.10010; M54#10135; R1973,6V304

[4] Some properties of numbers M, N and L, Glasnik Mat., 14 (34) (1979), no. 2, 201-211.
Z429.10006; M83c:10019; R1980,8A85

UHLER H.S.,
[1] The coefficients of Stirling's series for $\log \Gamma(x)$. Proc. Nat. Acad. Sci., 28 (1942), 59-62.
M3-275g

ULLOM S.V.,
[1] Upper bounds for p-divisibility of sets of Bernoulli numbers, J. Number Theory, 12 (1980), 197-200.
Z449.10009; M81h:10019; R1981,2A127

UNDERWOOD R.S.,
[1] An expression for the summation $\sum_{m=1}^n m^p$, Amer. Math. Monthly, 35 (1928), 424-428.
J54.104

URBANOWICZ J.,
[1] On the divisibility of generalized Bernoulli numbers. Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), pp. 711-728, Contemp. Math., 55, Amer. Math. Soc., Providence, R.I., 1986.
Z596.12002; M88b:11012; R1987,3A136

[2] On the divisibility of $w_{m+1}(F^+){\zeta}_{F^+}(-m)$ for cyclotomic fields F, Comm. Algebra, 16 (1988), no.7, 1315-1323.
Z661.12001; M89k:11100; R1988,11A366

[3] On the equation $f(1)1^k+f(2)2^k+ \cdots +f(x)x^k+R(x)=By^2$, Acta Arith., 51 (1988), no. 4, 349-368.
Z661.10026; M90b:11025; R1989,8A106

[4] Remarks on the equation $1^k+2^k+ \cdots +(x-1)^k=x^k$, Nederl. Akad. Wetensch. Indag. Math., 50 (1988), no. 3, 343-348.
Z661.10025; M90b:11026; R1989,2A89

[5] Connections between $B_{2,\chi}$ for even quadratic Dirichlet characters $\chi$ and class numbers of appropriate imaginary quadratic fields. I, II. Compositio Math., 75 (1990), no.3, 247-270, 271-285. Corrig.: Compositio Math., 77 (1991), no. 1, 119-125.
Z706.11058/9; M92a:11134a,b; R1991,3A215/216; 1991,8A433

[6] On the $2$-primary part of a conjecture of Birch-Tate. Acta Arith., 43 (1983),no. 1, 69-81.
Z529.12008; M85f:11080; R1984,8A297

[7] A generalization of the Lerch-Mordell formulas for positive discriminants. Colloq. Math., 59 (1990), no. 2, 197-202.
Z729.11050; M91m:11103

[8] On some new congruences between generalized Bernoulli numbers, I. Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, Années 1989/90-1990/91, No.4, 23pp., (1991).
Z748.11017; M93m:11111

[9] On some new congruences between generalized Bernoulli numbers, II. Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, 1989/90-1990/91, No.5, 24pp., (1991). Corrigendum ibid., 1992/93-1993/94, 3 pp.
Z748.11018; M93m:11111

[10] Remarks on the Stickelberger ideals of order 2. Algebraic $K$-theory, commutative algebra, and algebraic geometry. Proc. Joint US-Italy Seminar, Santa Margherita Ligure/Italy 1989, Contemp. Math., 126 (1992), 179-192.
Z756.11040; M93e:11139; R1993,7A290

[11] On Diophantine equations involving sums of powers with quadratic characters as coefficients, I. Compositio Math. 92 (1994), no. 3, 249-271.
Z810.11017; M96f:11054

[12] On Diophantine equations involving sums of powers with quadratic characters as coefficients. II. Compositio Math. 102 (1996), no. 2, 125-140.
Z960.35749; M97m:11047; R1997,10A186

URBANOWICZ J.: see also MOREE P., TE RIELE H.J.J., URBANOWICZ J.

URBANOWICZ J.: see also SCHINZEL A., URBANOWICZ J., VAN WAMELEN P.

URBANOWICZ J.: see also SZMIDT J., URBANOWICZ J.

URBANOWICZ J.: see also SZMIDT J., URBANOWICZ J., ZAGIER D.

USPENSKY J.V. (OUSPENSKY),
[1] Sur une série asymtotique d'Euler, Arch. der Math. und Phys. (3), 19 (1912), 370-371.
J43.343

USPENSKY J.V., HEASLET M.A.,
[1] Elementary number theory, New York, 1939, Ch. 9.
J65.1141; Z24,247; M1-38d

UZBANSKIJ V.M.,
[1] Dmitrij Grave i ego vremya [Dmitrij Grave and his time], Naukova Dumka, Kiev, 1998, 268 pp.


VALDEZ J.,
[1] A new property of the Bernoulli numbers, Math. Mag., 47 (1974), 144-145.
Z285.10010; M49#213; R1975,2A149

VALETTE A.,
[1] Le point sur la conjecture de Fermat, Bull. Soc. Math. Belgique, Ser. A, 39 (1987), 23-47.
Z636.10013; M89c:11049; R1988,12A448

VAN DEN BERG F.J.: see van den BERG F.J.

VAN DER POORTEN A.: see van der POORTEN A.

VAN DER WAALL R.W.: see van der WAAL R.W.

VANDIVER H.S.,
[1] On Bernoulli's numbers, Fermat's quotient and last theorem, Bull. Amer. Math. Soc. (2), 21 (1914), 68.
J45.290

[2] Symmetric functions of systems of elements in finite algebra and their connection with Fermat's quotient and Bernoulli's numbers (second paper), Bull. Amer. Math. Soc., 22 (1916), 380-381.
J46.191

[3] Symmetric functions formed by systems of elements of a finite algebra and their connection with Fermat's quotient and Bernoulli numbers, Ann. of Math., 18 (1917), no. 3, 105-114.
J46.1444

[4] A property of cyclotomic integers and its relation to Fermat's last theorem (third paper), Bull. Amer. Math. Soc., 24, (1918), 472-473.
J46.225

[5] On the first factor of the class number of a cyclotomic field, Bull. Amer. Math. Soc., 25 (1919), 458-461.
J47.151

[6] On Kummer's memoir of 1857 concerning Fermat's last theorem, Proc. Nat. Acad. Sci. U.S.A., 6 (1920), no. 5, 266-269.
J47.151

[7] On the class-number of the field $\Omega (e {{2 \pi i}\over{p^n}})$ and the second case of Fermat's last theorem, Proc. Nat. Acad. Sci. USA, 6 (1920), 416-421.
J47.151

[8] Note on some results concerning Fermat's last theorem, Bull. Amer. Math. Soc., 28 (1922), 258-260.
J48.1172

[9] On Kummer's memoir of 1857, concerning Fermat's last theorem, Bull. Amer. Math. Soc., 28 (1922), 400-407.
J48.1172

[10] A property of cyclotomic integers and its relations to Fermat's last theorem, 2, Ann. of Math. (2), 26 (1925), 217-232.
J51.136

[11] Note on trinomial congruences and the first case of Fermat's last theorem, Ann. of Math. (2), 27 (1925), 54-56.
J51.136

[12] Transformation of the Kummer criteria in connection with Fermat's last theorem, Ann. of Math., 27 (1926), 171-176.
J52.160

[13] Application of the theory of relative cyclic fields to both cases of Fermat's last theorem, Trans. Amer. Math. Soc., 28 (1926), 554-560.
J52.159

[14] Summary of results and proofs concerning Fermat's last theorem, Proc. Nat. Acad. Sci. USA, 12 (1926), 106-109; 767-773.
J52.159

[15] Application of the theory of relative cyclic fields to both cases of Fermat's last theorem, Trans. Amer. Math. Soc., 29 (1927), 154-162.
J53.147

[16] Transformation of the Kummer criteria in connection with Fermat's last theorem, Ann. of Math. (2), 28 (1927), 451-458 (second paper).
J53.148

[17] On Fermat's last theorem, Trans. Amer. Math. Soc., 31 (1929), no. 4, 613-642.
J55.701

[18] The extension of the Bernoulli summation formula, Amer. Math. Monthly, 36 (1929), 36-37.
J55.I.60

[19] Summary of results and proofs concerning Fermat's last theorem, 3, Proc. Nat. Acad. Sci. USA, 15 (1929), 43-48.
J55.130

[20] Summary of results and proofs concerning Fermat's last theorem, 4, Proc. Nat. Acad. Sci. USA, 15 (1929), 108-109.
J55.130

[21] Determination of some properly irregular cyclotomic fields, Proc. Nat. Acad. Sci. USA, 16 (1930), 139-150.

[22] Summary of results and proofs on Fermat's last theorem, Proc. Nat. Acad. Sci. USA, 16 (1930), 298-304.
J56.170

[23] On the second factor of the class number of a cyclotomic field, Proc. Nat. Acad. Sci. USA, 16 (1930), 743-749.
J56.887

[24] Note on the divisors of the numerators of Bernoulli's numbers, Proc. Nat. Acad. Sci. USA, 18 (1932), 954-957.
J58.I.180; Z5,344

[25] Fermat's last theorem and the second factor in the cyclotomic class number, Bull. Amer. Math. Soc., 40 (1934), 118-126.
J60.128; Z9,007

[26] A note on units in super-cyclic fields, Bull. Amer. Math. Soc., 40 (1934), 855-858.
J60.932; Z10,291

[27] On Bernoulli numbers and Fermat's last theorem, Miscellanea Amer. Philos. Soc. (1936).

[28] Note on a certain ring-congruence, Bull. Amer. Math. Soc., 43 (1937), 418-423.
J63.106; Z17,100

[29] On generalizations of the numbers of Bernoulli and Euler, Proc. Nat. Acad. Sci. USA, 23 (1937), 555-559.
J63.I.107; Z17,341

[30] On Bernoulli's numbers and Fermat's last theorem, Duke Math. J., 3 (1937), 569-584.
J63.II.895; Z18,005

[31] On analogues of the Bernoulli and allied numbers, Proc. Nat. Acad. Sci. USA, 25 (1939), 197-201.
J65.126; Z21,105

[32] On basis systems for groups of ideal classes in a properly irregular cyclotomic field, Proc. Nat. Acad. Sci. U.S.A., 25 (1939), no. 11, 586-591.
J65.109; Z22,110; M1-68d

[33] On Bernoulli's numbers and Fermat's last theorem (second paper), Duke Math. J., 5 (1939), 418-427.
J65.143; Z21,105

[34] On the composition of the group of ideal classes in a properly irregular cyclotomic field, Monatsh. Math., 48 (1939), 369-380.
J65.107; Z22,109; M1-68e

[35] Certain congruences involving the Bernoulli numbers, Duke Math J., 5 (1939), 548-551.
J65.126; Z21,390; M1-4d

[36] On general methods for obtaining congruences involving Bernoulli numbers, Bull. Amer. Math. Soc., 46 (1940), 121-123.
J66.139; Z23,007; M1-200a

[37] Simple explicit expressions for generalized Bernoulli numbers of the first order, Duke Math J., 8 (1941), 575-584.
M3-67a

[38] On improperly irregular cyclotomic fields, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), no. 1, 77-83.
M2-146h

[39] Certain congruence criteria connected with Fermat's theorem, Proc. Nat. Acad. Sci. USA, 28 (1942), 144-150.
M3-269f

[40] General congruences involving the Bernoulli numbers, Proc. Nat. Acad. Sci. USA, 28 (1942), 324-328.
M4-34f

[41] An arithmetical theory of the Bernoulli numbers, Trans. Amer. Math. Soc., 51 (1942), 502-531.
M4-34e

[42] Bernoulli's numbers and certain arithmetic quotient functions, Proc. Nat. Acad. Sci. USA, 31 (1945), 310-314.
Z63,975; M7-145f

[43] Fermat's quotient and related arithmetical functions, Proc. Nat. Acad. Sci. USA, 31 (1945), 55-60.
M6-170g

[44] Fermat's last theorem. Its history and the nature of the known results concerning it, Amer. Math. Monthly, 53 (1946), 555-578.
M8-313e

[45] New types of congruences involving Bernoulli numbers and Fermat's quotient, Proc. Nat. Acad. Sci. USA, 34 (1948), 103-110.
Z30,111; M9-412d

[46] On congruences which relate the Fermat and Wilson quotients to Bernouli numbers, Proc. Nat. Acad. Sci. USA, 35 (1949), 332-337.
Z33,351; M11-11d

[47] A supplementary note to a 1946 article on Fermat's last theorem, Amer. Math. Monthly, 60 (1953), 164-167.
Z51,280; M14-725a; R1953,54

[48] Les travaux mathématiques de Dimitry Mirimanoff, Enseign. Math., 39 (1953), 169-179.
Z50,2; M14-833f; R1955,2064

[49] The relation of some data obtained from rapid computing machines to the theory of cyclotomic fields, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), no. 6, 474-480.
Z56.41; M15-937c; R1955,1619

[50] Examination of methods of attack on the second case of Fermat's Last Theorem, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), no.8, 732-735.
Z56,41; M16-13f; R1955,1639

[51] On the divisors of the second factor of the class number of a cyclotomic field, Proc. Nat. Acad. Sci. USA, 41 (1955), 780-783.
M17-464a; R1956,4300

[52] Is there an infinity of regular primes?, Scripta Math., 21 (1955) (1956), 306-309.
Z71,44; R1957,2879

[53] On distribution problems involving the numbers of solutions of certain trinomial congruences, Proc. Nat. Acad. Sci. USA, 45 (1959), 1635-1641.
Z90,259; M22#4669; R1960,8579

[54] On developments in an arithmetic theory of the Bernoulli and allied numbers, Scripta Math., 25 (1961), 273-303.
Z100,269; M26#66; R1962,6A107

[55] Note on Euler number criteria for the first case of Fermat's Last Theorem. Amer. J. Math., 62 (1940), 79-82.
J66.152; Z22.307; M1-200d

VANDIVER H.S., WAHLIN G.E.,
[1] Algebraic numbers, 2, Report of the Comm. Alg. Numbers, Bull. Nat. Research Council, 1928, No. 62, 1-111.
J54.188

VANDIVER H.S.: see also LEHMER D.H., LEHMER E., VANDIVER H.S.

VANDIVER H.S.: see also SELFRIDGE J.L., NICOL C.A., VANDIVER H.S.

VANDIVER H.S.: see also STAFFORD E.T., VANDIVER H.S.

VAN VEEN S.C.: see van VEEN S.C.

VAN WAMELEN P.: see SCHINZEL A., URBANOWICZ J., VAN WA MELEN P.

VASAK J.T.,
[1] Periodic Bernoulli numbers and polynomials, Ph. D. Thesis, University of Illinois at Urbana-Champaign, 1979.

VASILEV M.V.,
[1] Relations between Bernoulli numbers and Euler numbers, Bull. Number Theory Related Topics, 11 (1987), no. 1-3, 93-95.
Z669.10021; M90g:11027

van VEEN S.C.,
[1] Asymptotic expansion of the generalized Bernoulli numbers $B\sb n\sp {(n-1)}$ for large values of $n(n$ integer), Nederl. Akad. Wetensch. Proc. Ser. A. 54 = Indagationes Math. 13 (1951), 335-341.
Z043.28503; M13,549a

VENKOV A.B.,
[1] Spectral theory for automorphic functions and its applications. Kluwer Acad. Publ., 1990, xvi+176pp.
Z719.11030; M93a:11046

VENKOV B.A.,
[1] Elementarnaya teoriya chisel [Elementary Number Theory]. Moskva-Leningrad, 1937, Ch. 2.7.
J43.343

[2] K rabote "O chislakh Bernulli" [On the paper "On Bernoulli numbers"]. In: Voronoi, G.F., Sobranie sochinenii v trekh tomakh. (Russian) [Collected works in three volumes.] Vol. I, Kiev, 1952, 392-393.
Z49,28; M16-2d; R1954,3228K

VERHEUL E.R.,
[1] A simple relation between Bernoulli sums. Nieuw Arch. Wisk. (4), 9 (1991), no. 3, 301-302.
Z769.11012; M93e:11031

VERLINDEN P.,
[1] $p$-adic Euler-Maclaurin expansions. Indag. Math. (N.S.) 7 (1996), no. 2, 257-270.
Z867.65024; M99d:41052; R1996,12A327

VIENNOT G.,
[1] Interprétations combinatoires des nombres d'Euler et de Genocchi. Séminaire de Théorie des nombres, Univ. Bordeaux I, année 1981-82, 1982, exp. no. 11, 94 pp.
Z505.05006; M84i:10013

VIENNOT G.: see also FRANÇON J., VIENNOT G.

VIENNOT G.: see also DUMONT D., VIENNOT G.

DE VILLIERS J.M.: see DE BRUYN G.F.C., DE VILLIERS J.M.

VLADIMIROV V.S., VOLOVICH I.V., ZELENOV E.I.,
[1] Spectral theory in p-adic quantum mechanics and the theory of representations, (Russian) Izv. Akad. Nauk. SSSR Ser. Mat. 54 (1990), no. 2, 275-302.
Z(715.22029)709.22010; M91f:81051

VOINOV V., NIKULIN M.,
[1] Generating functions, problems of additive number theory, and some statistical applications. Rev. Roumaine Math. Pures Appl., 40 (1995), no. 2, 107-147.
Z881.05011; R1997,3V214

VOLKENBORN A.,
[1] Ein p-adisches Integral und seine Anwendungen, Köln, Dissert., 1971.
Z245.10044*

[2] Ein p-adisches Integral und seine Anwendungen, I, Manuscr. Math., 7 (1972), 341-473.
Z245.10045; M49#2670; R1973,3B205

[3] Ein p-adisches Integral und seine Anwendungen, II, Manuscr. Math. 12 (1974), 17-46.
Z276.12018; M48#11064

VOLOVICH I.V.: see VLADIMIROV V.S., VOLOVICH I.V., ZELENOV E.I.

VON RANDOW R.: see MEYER W., VON RANDOW R.

VOORHOEVE M.: see GYÖRY K., TIJDEMAN R., VOORHOEVE M.

VORONOI G.F.,
[1] O chislakh Bernulli [On Bernoulli numbers]. Soobshcheniya Khar'kovsk. Mat. obshch. (2), 2 (1889), 129-148. Also in: Sobranie sochinenii v trekh tomakh. (Russian) [Collected works in three volumes.] Vol. I, Kiev, 1952, 7-23.
J12.268; Z49,28; M16-2d; R1954,3228K

[2] Ob opredelenii summy kvadratichnykh vychetov prostogo $p$ vida $4m+3$ pri pomoshchi chisel Bernulli [On the determination of the sum of quadratic residues of a prime $p$ of the form $4m+3$ by means of Bernoulli numbers]. Protokoly Sankt Petersb. mat. obshch, 5 (1899). Also in: Sobranie sochinenii v trekh tomakh. (Russian) [Collected works in three volumes.] Vol. III, Kiev, 1953, 203-204.
Z49,28; M16-2d; R1954,3228K

VORONOI G.F.: see also KISELEV A.A. [4]

VOROS A.,
[1] Spectral functions, special functions and the Selberg zeta function. Commun. Math. Phys., 110 (1987), no. 3, 439-465.
Z631.10025; M89b:58173; R1987,11A535

[2] Spectral zeta functions. In: Zeta functions in geometry (Tokyo, 1990), 327-358, Adv. Studies in Pure Math., 21, Kinokuniya, Tokyo, 1992.
Z819.11033; M94h:58176; R1994,9A386

VOROS A.: see also BALAZS N.L., SCHMIT C., VOROS A.

VOSE M.D.,
[1] The distribution of divisors of $N!$, Acta Arith., 50 (1988), no. 2, 203-209.
Z647.10038; M89j:11082; R1988,11A97

VOSKRESENSKII V.E.,
[1] Calculation of local volumes in the Siegel-Tamagawa formula. Engl. Transl. in: Math. USSR-Sb., 66 (1990), no. 2, 447-460.
Z691.10014; M90h:11055

VOSTOKOV S.V.,
[1] A remark on the space of cyclotomic units. Engl. Transl. in: Vestnik Leningrad Univ. Math., 21 (1988), no. 1, 16-20.
Z649.12013; M89f:11150; R1988,7A356

[2] Artin-Hasse exponentials and Bernoulli numbers. (Russian) Trudy S.-Peterburg. Mat. Obshch. 3 (1995), 185--193, 324. English translation: Amer. Math. Soc. Transl. (2), 166 (1995), 149-156.
Z855.11059; M97c:11110; R1987,8A241

VU THEINNU H.: see APOSTOL T.M., VU THEINNU H.


WAALL R.W. van der,
[1] On a property of $\tan x$, J. Number Theory, 5 (1973), 242-244.
Z266.10014; M48#8375

WADA H.,
[1] Some computations on the criteria of Kummer, Tokyo J. Math., 3 (1980), no. 1, 173-176.
Z448.10016; M81m:10028; R1981,2A128

WAGON S.,
[1] Fermat's last theorem, Math. Intelligencer, 8 (1986), no. 1, 59-61.
M87e:11045; R1986,8A102

WAGSTAFF S.S. JR.,
[1] Zeros of p-adic L-functions, Math. Comp., 29 (1975), no. 132, 1138-1143.
Z315.12009; M52#8096; R1976,9A369

[2] The irregular primes to 125000, Math. Comp., 32 (1978), no. 142, 583-591.
Z377.12002; M58#10711; R1979,1A164

[3] Proof of a formula of Ramanujan concerning Bernoulli numbers, Notices Amer. Math. Soc., 26 (1979), A-330.

[4] p-divisibility of certain sets of Bernoulli numbers, Math. Comp., 34 (1980), no. 150, 647-649.
Z424.10013; M81i:10018; R1980,11A67

[5] Zeros of p-adic L-functions, 2, Number Theory Related to Fermat's Last Theorem (N. Koblitz, ed.), Progress in Math., No. 26, Birkhäuser, Boston, Mass., 1982, 297-308.
Z498.12015; M84h:12027; R1985,4A335

[6] Ramanujan's paper on Bernoulli numbers, J. Indian Math. Soc. N.S.(9), 45 (1981), no. 1-4, 49-65 (1984).
Z636.10010; M87h:11019; R1956,8V689

WAGSTAFF S.S., JR., TANNER J.W.,
[1] New congruences for the Bernoulli numbers, Math. Comp., 48 (1987), no. 177, 341-350.
Z613.10012; M87m:11017

WAGSTAFF S.S. JR.: see also ERDÖS P., WAGSTAFF S.S.

WAGSTAFF S.S. JR.: see also TANNER J.W., WAGSTAFF S.S.

WAHLIN G.E.: see VANDIVER H.S., WAHLIN G.E.

WALDSCHMIDT M., MOUSSA P., LUCK J.-M., ITZYKSON C. (Eds.),
[1] From Number Theory to Physics. Springer-Verlag, Berlin etc., 1992, xiv+690 pp.
Z790.11061; M93m:11001

WALTON W.,
[1] On certain transformations in the calculus of operations, Quart. J. Pure Appl. Math., 8 (1867), 222-227.

WALUM H.,
[1] Multiplication formulae for periodic functions, Pacific J. Math., 149 (1991), no. 2, 383-396.
Z736.11012; M92c:11019

van WAMELEN P.: see SCHINZEL A., URBANOWICZ J., VAN WAMELEN P.

WANG CHUNG LIE, WANG XING HUA,
[1] Refinements of the Mathieu inequality. (Chinese. English summary). J. Math. Res. Exposition, 1 (1981), no. 1, 107-112.
Z476.26008; M83j:26017; R1982,4B3

WANG GUAN MIN,
[1] An identity for proper Dirichlet series and Euler numbers (Chinese. English and Chinese summaries). Zhangzhou Shiyuan Xuebao (Ziran Kexue Ban), 8 (1994), no. 4, 85-8 8.

[2] Rao-Davis identities related to the Riemann zeta-function. (Chinese. English, Chinese summary). Zhangzhou Shiyuan Xuebao (Ziran Kexue Ban) 10 (1996), no. 2, 28-41, 47.
M97g:11091

WANG KAI,
[1] A proof of an identity of the Dirichlet L-functions, Bull. Inst. Math., Acad. Sin., 10 (1982), no. 3, 317-321.
Z497.10031; M84c:10040

[2] Exponential sums of Lerch's zeta functions, Proc. Amer. Math. Soc., 9 (1985), no. 1, 11-15.
Z573.10011; M86j:11084; R1986,6A189

[3] A proof of an identity of the Dirichlet L-function at negative integers, Bull. Inst. Math., Acad. Sin., 13 (1985), no. 2, 143-147.
Z591.10032; M87a:11078

WANG SHUN HWA: see DE TEMPLE D.W., WANG SHUN HWA

WANG TIAN MING, ZHANG XIANG DE,
[1] Some identities related to Genocchi numbers and the Riemann zeta-function, J. Math. Res. Exposition, 17 (1997), no. 4, 597-600.
Z902.11011; R1996,11V258

WANG TIANMING, ZHANG ZHIZHENG,
[1] Recurrence sequences and Nörlund-Euler polynomials, Fibonacci Quart., 34 (1996), no. 4, 314-319.
Z861.11011; M97c:11024

WANG XING HUA: see WANG CHUNG LIE, WANG XING HUA

WANG Z.X., GUO D.R.,
[1] Special functions. World Scientific, Singapore, etc., 1989, xviii+695pp.
Z724.33001; M91a:33001

WASHINGTON L.C.,
[1] A note on p-adic L-functions, J. Number Theory, 8 (1976), no. 2, 245-250.
Z329.12017; M53#10766; R1977,2A410

[2] The calculation of $L_p(1,chi)$, J. Number Theory, 9 (1977), no. 2, 175-178.
Z363.12019; M55#12704; R1977,11A145

[3] The non-p-part of the class number in a cyclotomic $ Z_p$-extension, Invent. Math., 49 (1978), no. 1, 87-97.
Z403.12007; M80c:12005; R1979,4A397

[4] Euler factors for p-adic L-functions, Mathematika, 25 (1978), no. 1, 68-75.
M58#22025

[5] Kummer's calculation of $L_p(1,{\chi})$, J. Reine Angew. Math., 305(1979), 1-8.
Z398.12019; M80e:12017; R1979,8A80

[6] Units of irregular cyclotomic fields, Illinois J. Math., 23 (1979), no. 4, 635-647.
Z423.12005; 427.12004; M81a:12006; R1980,7A312

[7] Zeros of p-adic L-functions, Sém. théor. nombres, 1980-81, Univ. Bordeaux I, Talence, 1981, Exp. No. 25, 4 pp.
Z479.12005; M82m:10006; R1985,4A334

[8] p-adic L-functions at $s=0$ and $s=1$, Analytic number theory, Lect. Notes in Math., 899 (1981), 166-170.
Z479.12004; M83m:12019

[9] The derivative of p-adic L-functions, Acta. Arith., 40 (1981), no. 1, 109-115.
Z483.12001; M83m:12020; R1982,10A298

[10] Introduction to cyclotomic fields, New York, Springer-Verlag, 1982.
Z484.12001*; M85g:11001; R1982,12A356K; 1983,4A368K

[11] Recent results on cyclotomic fields, Algebraic Topology, 1981, Sem. notes, Inst. of Math., Univ. of Aarhus, 1982, No. 1, 120-129.
Z502.12003; M83k:12003; R1983,7A154

[12] Zeroes of p-adic L-functions, Progress in Math., Boston, No. 22, (1982), 337-357 (Théor. des Nombres. Paris, 1980-81, Sémin. Delange-Pisot-Poitou).
Z495.12015; M84f:12008; R1985,4A334

[13] On some cyclotomic congruences of F. Thaine, Proc. Amer. Math. Soc., 93 (1985), no. 1, 10-14.
Z564.10010; M86c:11019; R1986,2A331

[14] On Sinnott's proof of the vanishing of the Iwasawa invariant $\mu_p$. Algebraic number theory, 457-462, Adv. Stud. Pure Math., 17, Academic Press, Boston, MA, 1989.
Z732.11059; M92e:11123

[15] Introduction to cyclotomic fields. Second edition. Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1997. xiv+487 pp.
Z970.07078; M97h:11130

[16] $p$-adic $L$-functions and sums of powers, J. Number Theory, 69 (1998), no. 1, 50-61.
Z910.11047; M99a:11134

WASHINGTON L.C.: see also ADLER A., WASHINGTON L.C.

WASHINGTON L.C.: see also FERRERO B., WASHINGTON L.C.

WASHINGTON L.C.: see also FRIEDMAN E., SANDS J. W.

WATSON G.N.,
[1] Theorems stated by Ramanujan (II): Theorems on summation of series, J. London Math. Soc., 3 (1928), 216-225.
J54.229

WATSON G.N.: see also ADIGA C., BERNDT B.C. et al.

WATSON G.N.: see also WHITTAKER E.T., WATSON G.N.

WEIHRAUCH K.,
[1] Untersuchungen über eine Gleichung des ersten Grades mit mehreren Unbekannten, Diss. Dorpat, 1869.
J2.51

[2] Die Anzahl der Lösungen diophantischer Gleichungen bei theilfremden Coefficienten, Zeitsch. für Math., 20 (1875), 97-111.
J7.93

[3] Über die Ausdrücke $\sum f_n(m)$ und die Umgestaltungen der Formel für die Lösungsanzahlen Anwendung der Formel in der Combinationslehre, Zeitsch. für Math., 20 (1875), 112-117.
J7.93

[4] Anzahl der Auflösungen einer unbestimmten Gleichung für einen speciellen Fall von nicht theilfremden Coefficienten, Zeitsch. für Math., 20 (1875), 314-316.
J7.93

[5] Anzahl der Lösungen für die allgemeinste Gleichung ersten Grades mit vier Unbekannten, Zeitsch. für Math., 22 (1877), 234-244.
J9.134

[6] Theorie der Restreihen zweiter Ordnung, Zeitsch. für Math., 32 (1887), 1-21.
J19.179

WEIL A.,
[1] L'oeuvre arithmétique d'Euler. "Leonhard Euler. 1707-1783: Beiträge zu Leben und Werk", Birkhäuser, Basel, 1983, 111-134.
Z516.01012; M84m:01021; R1984,7A13

[2] Number Theory. An Approach Through History From Hammurapi to Legendre. Birkhäuser, Boston etc., 1984, xxi + 375pp.
Z531.10001; M85c:01004

WEINMANN A.,
[1] Asymptotic expansions of generalized Bernoulli polynomials, Proc. Camb. Phil. Soc., 59 (1963), no. 1, 73-80.
Z114,34; M29#5009; R1963,10B66

WEISS A.: see RITTER J., WEISS A.

WESTLUND J.,
[1] On the class number of the cyclotomic number field $k(e{{2 \pi i}\over{p^n})$, Trans. Amer. Math. Soc., 4 (1903), 201-212.
J34.237

WHITTAKER E.T., WATSON G.N.,
[1] A Course of Modern Analysis, 4th Edition. Cambridge University Press, Cambridge, 1927.
J53,180

WICKE F.,
[1] Über ultra-Bernoullische und ultra-Eulersche Zahlen und Funktionen und deren Anwendung auf die Summation von Reihen, Diss. Jena, 1905, 68 p.
J36.498

WIEFERICH A.,
[1] Zum letzten Fermatschen Theorem, J. Reine Angew. Math., 136 (1909), no. 4, 293-302.
J40.256

WILES A.,
[1] Modular curves and the class group of $Q(\zeta_p)$, Invent. Math., 58 (1980), no. 1, 1-35.
Z436.12004; M82j:12009; R1980,10A274

WILES A.: see also MAZUR B., WILES A.

WILES A.: see also RUBIN K., WILES A.

WILKINSON K.M.: see RUDOLFER S.M., WILKINSON K.M.

WILLIAMS G.T.,
[1] A new method of evaluating ${\zeta}(2n)$, Amer. Math. Monthly, 60 (1953), no. 1, 19-25.
Z50,68; M14,536j; R1953,31

WILLIAMS H.: see BEACH B., WILLIAMS H., ZARNKE C.

WILLIAMS H.C.: see FUNG G., GRANVILLE A., WILLIAMS H.C.

WILLIAMS H.C.: see STEPHENS A.J., WILLIAMS H.C.

WILLIAMS K.P.,
[1] Relating to some determinants connected with the Bernoulli numbers, Amer. Math. Monthly, 23 (1916), 263-266.

WILLIAMS K.S.,
[1] On $\sum_{n=1}^\infty (1/n^{2k})$, Math. Mag., 44 (1971), no. 5, 273-276.
Z224.40008; M45#3997; R1972,6B17

[2] Bernoulli's identity without calculus. Math. Mag. 70 (1997), no. 1, 47-50.
Z880.11023; M98c:05015

WILLIAMS K.S., ZHANG NAN-YUE,
[1] Special values of the Lerch zeta-function and the evaluation of certain integrals. Proc. Amer. Math. Soc., 119 (1993), no. 1, 35-49.
Z785.11046; M93k:11081

[2] Evaluation of two trigonometric sums, Math. Slovaca, 44 (1994), no. 5, 575-583.
Z820.11010; M96d:11088

[3] Values of the Riemann zeta function and integrals involving $\log(2\,{\rm sinh}(\theta/2))$ and $\log(2\sin(\theta/2))$, Pacific J. Math. 168 (1995), no. 2, 271-289.
Z828.11041; M96f:11170

WILLIOT V.,
[1] Note sur le procédé le plus simple de calcul des nombres de Bernoulli, Bull. Soc. Math. France, 16 (1888), 144-149.
J20.265

WILSON B.M.: see BERNDT B.C. et al.

WILSON J.C.,
[1] On Franel-Kluyver integrals of order three, Acta Arith., 66 (1994), no. 1, 71-87.
Z807.11013; M94m:11116; R1997,12A60

WILSON J.C.: see also HALL R.R. et al.

WILTON J.R.,
[1] A proof of Burnside's formula for $log {\Gamma}(x+1)$ and certain allied properties of Riemann's $\zeta$-function, Messeng. Math. (2), 52 (1923), 90-93.
J48.409

WOLFF H.,
[1] Über die Anzahl der Zerlegungen einer ganzen Zahl in Summen, Diss. Halle, 1899.
J30.201

WONG E.: see also BORWEIN J.M., WONG E.

WONG R., ZHANG J.-M.,
[1] Asymptotic monotonicity of the relative extrema of Jacobi polynomials, Canad. J. Math., 46 (1994), no. 6, 1318-1337.
Z819.33004; M95j:33029

WOODCOCK C.F.,
[1] An invariant p-adic integral on $ Z_p$, J. London Math. Soc., (2), 8 (1974), 731-734.
Z292.12021; M50#4545; R1975,6A461

[2] A note on some congruences for the Bernoulli numbers $B_m$, J. London Math. Soc. (2), 11 (1975), no. 2, 256.
Z335.10017; M56#5415; R1976,3A162

[3] A two variable Riemann zeta function, J. Number Theory, 27 (1987), no. 2, 212-221.
Z623.10028; M88k:11057; R1988,3B32

WOOLRIDGE K.,
[1] Some results in Arithmetical Functions Similar to Euler's Phi-Function, Ph.D. thesis, Univ. of Illinois, 1975. Ch. III: Numerical Data on Irregular Primes, 32-41.

WOON S.C.,
[1] A tree for generating Bernoulli numbers, Math. Mag. 70 (1997), no. 1, 51-56.
Z882.11014; M98a:11026

WORONTZOF M.M. (WORONTZOFF M.),
[1] On the generalization of certain formulae investigated by Mr. Blissard, Quart. J. Math., 8 (1867), 185-208, 310-319.

[2] Sur les nombres de Bernoulli, Nouv. Ann. Math. (2), 15 (1876), 12-19.
J8.146

WORPITZKY J.,
[1] Studien über die Bernoullischen und Eulerschen Zahlen, J. Reine Angew. Math., 94 (1883), 203-232.
J15.201

[2] Über die Partialbruchzerlegung der Functionen, mit besonderer Anwendung auf die Bernoulli'schen, Zeit. für Math. und Phys., 29 (1884), 45-54.
J16.394

WRIGGE S.,
[1] Calculation of the Taylor series expansion coefficients of the Jacobian elliptic unction sn(x,k), Math. Comp. 37 (1981), no. 156, 495-497.
Z479.33003; M82d:65023

[2] An analytic disproof of Robertson's conjecture, J. Math. Anal. Appl., 154 (1991), no. 1, 80-82.
Z739.30002; M92a:05012

WRIGHT E.M.: see HARDY G.H., WRIGHT E.M.

WU YUN FEI,
[1] A computational formula for a class of identities involving Bernoulli polynomials, Math. Practice Theory, 1995, no. 2, 32-36.
M96j:11022; R1996,2A102


XIN XIAO LONG, ZHANG JIAN KANG,
[1] Some identities connecting Euler numbers and Bernoulli numbers (Chinese), Pure Appl. Math., 9 (1993), no. 1, 23-28.
Z849.11022; M94j:11024

YAGER R.I.,
[1] A Kummer criterion for imaginary quadratic fields, Compos. Math., 47 (1982), no. 1, 31-42.
Z506.12008; M83k:12008; R1983,2A276

YAGISHITA K.,
[1] On the Diophantine equation $\alpha^l + \beta^l = c \gamma^l$, TRU Math., 7 (1971), 5-10.
Z256.10014; M46#7161; R1973,5A149

YALAVIGI C.C.,
[1] Bernoulli and Lucas numbers, Math. Education, 5 (1971), A99-A102.
M46#131

YAMADA M.,
[1] An experimental theory of numbers (The prime factors of the numerators of Bernoulli numbers), J. Fac. Eng. Ibaraki Univ., 35 (1987), 159-170.
R1988.10A111

[2] An approach to Wieferich's condition, C. R. Math. Rep. Acad. Sci. Canada, 13 (1991), no. 2-3, 87-92.
Z731.11019; M92f:11052

YAMAGUCHI I.,
[1] On Fermat's last theorem, TRU Math., 3 (1967), 13-18.
Z167,316; M36#6350; R1968,10A91

[2] On generalized Fermat's last theorem, TRU Math., 6 (1970), 29-32.
Z242.10009; M46#8974; R1973,11A168

[3] On a property of the irregular class group in a properly $l$-th cyclotomic field, TRU Math., 7 (1971), 21-24.
Z252.12004; M47#3352; R1973,5A357

[4] On a Bernoulli numbers conjecture, J. Reine Angew. Math., 288 (1976), 168-175.
Z333.10005; M54#12628; R1977,6A100

[5] On the units in a $l^\nu$-th cyclotomic field, TRU Math., 13 (1977), no. 2, 1-12.
Z379.12003; M58#584; R1978,10A250

[6] Sympathetic Number Theory - The beautiful cyclotomic fields theory and Bernoulli numbers (Japanese), Sangyotosho Co. Ltd., 1994.

YAMAMOTO S.: see SHIRATANI K., YAMAMOTO S.

YANG BI CHENG,
[1] Formulas for sums of homogeneous powers of natural numbers related to the Bernoulli numbers (Chinese). Math. Practice Theory, 1994, no. 4, 52-56, 74.
M96c:11026

YANG BI CHENG, ZHU YUN HUA,
[1] Inequalities for the Hurwitz zeta-function on the real axis (Chinese), Acta Sci. Natur. Univ. Sunyatseni 36 (1997), no. 3, 30-35.
M99h:11101

YANG BI CHENG: see also ZHU YUN HUA, YANG BI CHENG,

YANG HUI,
[1] The operator l and its applications. I. A generalization of the Bernoulli polynomials, J. Math. (Wuhan), 1 (1981), no. 2, 195-206. (Chinese. English summary.)
Z519.33010; M83k:39004

YOKOI H.,
[1] On the distribution of irregular primes, J. Number Theory, 7 (1975), 71-76.
Z297.10034; M51#385; R1976,7A180

YOKOYAMA S.: see SHIRATANI K., YOKOYAMA S.

YOSHIDA H.,
[1] On absolute CM-periods. II, Amer. J. Math. 120 (1998), no. 6, 1199-1236.

YOSHIDA M.,
[1] A representation of the Bernoulli numbers $B_n$ and the tangent numbers $T_n$. SUT J. Math., 26 (1990), no. 2, 207-219.
Z746.11013; M92k:11021; R1991,11V421

YOUNG N.E.: see MILLAR J., SLOANE N.J.A., YOUNG N.E.

YOUNG P.T.,
[1] Congruences for Bernoulli, Euler, and Stirling numbers. J. Number Theory, 78 (1999), no. 2, 204-227.

YOUNG R.M.: see NUNEMACHER J., YOUNG R.M.

YU JING,
[1] A cuspidal class number formula for the modular curves $X_1(N)$, Math. Ann., 252 (1980), no. 3, 197-216.
Z426.12003; 436.12002; M82b:10030; R1981,6A377

[2] Transcendence and special zeta values in characteristic $p$. Ann. Math. (2), 134 (1991), no. 1, 1-23.
Z734.11040; M92g:11075

YU JING, YU JIU-KANG,
[1] A note on a geometric analogue of Ankeny-Artin-Chowla's conjecture, Number theory (Tiruchirapalli, 1996), 101-105, Contemp. Math., 210, Amer. Math. Soc., Providence, RI, 1998.
Z896.11047; M98g:11131

YÜ WÊN CH'ING: see EIE MINKING

ZAGIER D.B.,
[1] Valeurs des fonctions zêta des corps quadratiques réels aux entiers négatifs. Journées Arithmétiques de Caen (Univ. Caen, 1976), pp. 135-151. Astérisque No. 41-42, Soc. Math. France, Paris, 1977.
Z359.12012; M56#316; R1977,12A140

[2] Zetafunktionen und quadratische Körper. Eine Einführung in die höhere Zahlentheorie. Springer-Verlag, Berlin, 1981. viii + 144 pp.
Z459.10001; M82m:10002; R1982,3A107

[3] Hyperbolic manifolds and special values of Dedekind zeta-functions, Sonderforschungsbereich 40 Theor. Math., Univ. Bonn, 1984.

[4] Hyperbolic manifolds and special values of Dedekind zeta-functions, Invent. Math., 83 (1986), no. 2, 285-301.
Z591.12014; M87e:11069; R1986,6A500

[5] Periods of modular forms and Jacobi theta functions. Max-Planck-Institut für Math. Bonn, MPI/89-56, 15 pp.

[6] Periods of modular forms and Jacobi theta functions, Invent. Math., 104 (1991), no. 3, 449-465.
Z742.11029; M92e:11052

[7] On the values at negative integers of the zeta-function of a real quadratic field. Enseignement Math. (2), 22 (1976), 55-95.
Z334.12021; M53#10742; R1976/77,12A163

[8] Polylogarithms, Dedekind zeta functions, and the algebraic $K$-theory of fields. Arithmetic algebraic geometry, Proc. Conf., Texel/Neth. 1989, Prog. Math., 89 (1991), 391-430.
Z728.11062; M92f:11161

[9] Elementary aspects of the Verlinde formula and of the Harder- Narasimhan-Atiyah-Bott formula. Max-Planck-Institut für Math., Bonn, 1994, no.5, 16 pp.

[10] A modified Bernoulli number, Nieuw Arch. Wisk. (4), 16 (1998), no. 1-2, 63-72.
M99i:11013

ZAGIER D.: see also KOHNEN W., ZAGIER D.

ZAGIER D.: see also HALL R.R., WILSON J.C., ZAGIER D.

ZARNKE C.: see BEACH B., WILLIAMS H., ZARNKE C.

ZECH TH.,
[1] Potenzsummen und Bernoullische Zahlen, Z. Angew. Math. Mech., 34 (1954), 119-120.
Z56.13; M15-855e; R1955,838

ZEITLIN D.,
[1] Remarks on a formula for preferential arrangements, Amer. Math. Monthly, 70 (1963), 183-187.
Z116,11; M26#4928; R1964,12A143

[2] On the sums $\sum_{k=0}^nk^p$ and $\sum_{k=0}^n(-1)^kk^p$, Proc. Amer. Math. Soc., 15 (1964), 642-647.
Z123,1; M29#5010; R1967,1V164

ZELENOV E.I.: see VLADIMIROV V.S. et al.

ZELLER CHR.,
[1] De numeris Bernoulli eorumque compositione ex numeris integritis et reciprocis primis, Bull. sci. math. et astr., 5 (1881), 195-215.
J13.190

ZENG JIANG,
[1] Sur quelques propriétés de symétrie des nombres de Genocchi. (French) [On some symmetry properties of Genocchi numbers] Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993). Discrete Math. 153 (1996), no. 1-3, 319-333.
Z870.05002; M97k:05015

ZENG J.: see also DUMONT D., ZENG J.

ZENG J.: see also HAN GUO-NIU, ZENG JIANG

ZENG J.: see also HAN G.-N.; RANDRIANARIVONY A.; ZENG J.

ZHANG JIAN KANG: see XIN XIAO LONG, ZHANG JIAN KANG

ZHANG J.-M.: see WONG R., ZHANG J.-M.

ZHANG N.Y.,
[1] A representation of Riemann's zeta-function (Chinese), J. Math. Res. Exposition (1982), no. 4, 119-120.
Z506.10033; M84c:10037

[2] The Euler constant and some sums associated with the zeta function. (Chinese). Math. Practice Theory, (1990), no. 4, 62-70.
M92a:11098

ZHANG N.Y.: see also WILLIAMS K.S., ZHANG N.Y.

ZHANG PING: see SAGAN B.E., ZHANG PING

ZHANG R.: see GOSPER R.W., ISMAIL M.E.H., ZHANG R.

ZHANG WENPENG,
[1] On the several identities of Riemann zeta-function, Chinese Sci. Bull., 36 (1991), no. 22, 1852-1856.
Z755.11026; M92m:11086

[2] Some identities for Euler numbers (Chinese), J. Northwest Univ., 22 (1992), no. 1, 17-20.
Z886.11011 M93h:11024

[3] Some identities involving the Euler and the central factorial numbers, Fibonacci Quart. 36 (1998), no. 2, 154-157.

ZHANG XIANG DE: see WANG TIAN MING, ZHANG XIANG DE

ZHANG XIAN KE,
[1] A congruence formula for the class number of a general fourth degree cyclic field, Kexue Tongbao (Chinese), 32 (1987), no. 23, 1761-1763.
M89g:11101

[2] Congruences of class numbers of general cubic cyclic number fields (Chinese. English summary). J. China Univ. Sci. Tech., 17 (1987), no. 2, 141-145.
Z631.12003; M88i:11076; R1987,12A291

[3] Congruences for class numbers of general cyclic quartic fields, Kexue Tongbao (Science Bulletin), 33 (1988), no. 22, 1845-1848.

[4] Congruences modulo 8 for class numbers of general quadratic fields $ Q(\sqrt{m})$ and $ Q(\sqrt{-m})$, J. Number Theory, 32 (1989), no. 3, 332-338.
Z693.12005; M90k:11137

[5] Ten formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic quartic fields, Sci. China Ser. A, 32 (1989), no. 4, 417-428.
Z669.12005; M91b:11112

ZHANG ZHIZHENG,
[1] Relation between two kinds of numbers and its applications, Gongcheng Shuxue Xuebao 13 (1996), no. 1, 114-116.
M97g:11017; R1997,3V221

ZHANG ZHIZHENG, GUO LIZHOU,
[1] Recurrence sequences and Bernoulli polynomials of higher order, Fibonacci Quart., 33 (1995), no. 4, 359-362.
Z831.11023; M96c:11027; R1996,5A119

ZHANG ZHIZHENG, JIN JINGYU,
[1] Some identities involving generalized Genocchi polynomials and generalized Fibonacci-Lucas sequences, Fibonacci Quart., 36 (1998), no. 4, 329-334.

ZHANG ZHIZHENG: see also WANG TIANMING, ZHANG ZHIZHENG

ZHENG ZHIYONG,
[1] The Petersson-Knopp identity fo the homogeneous Dedekind sums, J. Number Theory, 57 (1996), no. 2, 223-230.
Z847.11021; M97c:11050

ZHBIKOVSKII A.K.,
[1] Teorema Silvestra otnositel'no bernullievykh chisel [Sylvester's theorem concerning Bernoulli numbers]. Vestnik matem. nauk, 1 (1862), no. 13, 109-110.

[2] K teorii chisel Bernulli [On the theory of Bernoulli numbers]. Mat. Sbornik, 10 (1882), no. 2, 127-166.

ZHU YUN HUA, YANG BI CHENG,
[1] An improvement of Euler's summation formula and some inequalities for sums of powers (Chinese), Acta Sci. Natur. Univ. Sunyatseni 36 (1997), no. 4, 21-26.
Z902.40002; M99i:40003

ZHU YUN HUA: see also YANG BI CHENG, ZHU YUN HUA

ZIA-UD-DIN M.,
[1] Recurrence formulae for Bernoulli's numbers, Math. Student, 3 (1935), 141-151.
J61.II.985; Z14.102

ZIMMER H.G.,
[1] Computational problems, methods and results in algebraic number theory, New York, Lecture Notes in Math., No. 262, 1972.
Z231.12001*; M48#2107; R1972,10A225

ZUBER M.,
[1] Propriétés de congruence de certaines familles classiques de polynômes, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 8, 869-872.
Z762.11005; M94b:11025

[2] Propriétés $p$-adiques de polynômes classiques, Thèse, Université de Neuchatel, 1992.

[3] Suites de Honda, Ann. Math. Blaise Pascal 2 (1995), no. 1, 307-314.
Z833.46062; M96k:11143


Back to Index