# Bernoulli Bibliography

This file contains, in reverse chronological order, all items that were added to the bibliography in 1999. For references to the reviewing journals, see the main bibliography.
November 12, 1999:

KIM HAN SOO, KIM TAEKYUN,
[6] Remark on $p$-adic $q$-Bernoulli numbers. Algebraic number theory (Hapcheon/Saga, 1996). Adv. Stud. Contemp. Math. 1 (1999), 127-136.

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

POPOV B. S.,
[1] Expressions of Laguerre polynomials through Bernoulli polynomials. Mat. Bilten No. 22, (1998), 15-18.

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).

YOUNG P.T.,
[1] Congruences for Bernoulli, Euler, and Stirling numberbs. J. Number Theory, 78 (1999), no. 2, 204-227.

LAN YIZHONG,
[1] A limit formula for $\zeta(2k+1)$. J. Number Theory, 78 (1999), no. 2, 271-286.

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

FUKUHARA S.,
[2] Generalized Dedekind symbols associated with the Eisenstein series. Proc. Amer. Math. Soc. 127 (1999), no. 9, 2561-2568.

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

HAN GUO-NIU,
[2] Symétries trivariés sur les nombres de Genocchi. European J. Combin. 17 (1996), no. 4, 397--407.

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.

September 10, 1999:

[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.

KIM E.E., TOOLE B.A.,
[1] Ada and the first computer. Scientific American, May 1999, 76-81.

MACLEOD R.A.,
[1] Fractional part sums and divisor functions, J. Number Theory 14 (1982), no. 2, 185-227.

GESSEL I.,
[4] Generating functions and generalized Dedekind sums, Electron. J. Combin. 4 (1997), no. 2, Research Paper 11, approx. 17 pp. ( electronic).

HALBRITTER U.,
[4] Some new reciprocity formulas for generalized Dedekind sums, Resultate Math. 8 (1985), no. 1, 21-46.

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

August 19, 1999:

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

KANEKO M.,
[3] Multiple zeta values and poly-Bernoulli numbers (Japanese), Seminar Reports of the Department of Mathematics, Tokyo Metropolitan University, 1997, 42 pp.

August 6, 1999:

HOFFMAN M. E.,
[2] Derivative polynomials for tangent and secant, Amer. Math. Monthly 102 (1995), no. 1, 23-30.

[3] Derivative polynomials, Euler polynomials, and associated integer sequences, Electron. J. Combin. 6 (1999), no. 1, Research Paper 21, 13 pp. (electron ic)

PORUBSKÝ S.,
[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.

RIORDAN J.,
[1] Inverse relations and combinatorial identities, Amer. Math. Monthly 71 1964, 485-498.

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.

ZUBER M.,
[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.

July 15, 1999:

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

APOSTOL T.M.,
[9] An elementary view of Euler's summation formula, Amer. Math. Monthly, 106 (1999), no. 5, 409-418.

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

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

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

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.

GOTO K.,
[1] A twisted adjoint $L$-value of an elliptic modular form, J. Number Theory 73 (1998), no. 1, 34-46.

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.

HUANG I-CHIAU, HUANG SU-YUN,
[1] Bernoulli numbers and polynomials via residues, J. Number Theory, 76 (1999), no. 2, 178-193.

ISHIBASHI M.,
[4] $\bold Q$-linear relations of special values of the Estermann zeta function, Acta Arith. 86 (1998), no. 3, 239-244.

[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.

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.

KURT V.,
[1] Remarks on higher-dimensional Dedekind sums, Math. Japon. 45 (1997), no. 2, 297-301.

LOUBOUTIN ST.,
[2] Computation of relative class numbers of imaginary abelian number fields, Experiment. Math. 7 (1998), no. 4, 293-303.

SASVÁRI Z.,
[1] An elementary proof of Binet's formula for the gamma function, Amer. Math. Monthly 106 (1999), no. 2, 156-158.

SAUZET O.,
[1] Théorie d'Iwasawa des corps $p$-rationnels et $p$-birationnels, Manuscripta Math. 96 (1998), no. 3, 263-273.

SHAFAREVICH I.R.,
[2] Selected chapters of algebra (Russian), Matem. obrazovanie, 1997, no. 2, 3-33.

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.

STRICHARTZ R.S.,
[1] Estimates for sums of eigenvalues for domains in homogeneous spaces, J. Funct. Anal. 137 (1996), no. 1, 152-190.

YOSHIDA H.,
[1] On absolute CM-periods. II, Amer. J. Math. 120 (1998), no. 6, 1199-1236.

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.

July 13, 1999:

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

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.

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

May 22, 1999:

LIU GUO DONG,
[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).

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

SATOH J.,
[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.

HAUSS M.,
[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.

TUAN VU KIM; NGUYEN THI TINH,
[3] Expressions of Legendre polynomials through Euler polynomials, Math. Balkanica (N.S.) 11 (1997), no. 3-4, 295-302.

March 12, 1999:

PFISTER F.,
[1] Bernoulli numbers and rotational kinematics, Trans. ASME J. Appl. Mech. 65 (1998), no. 3, 758-763.

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.

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

SATOH J.,
[4] Sums of products of two $q$-Bernoulli numbers, J. Number Theory, 74 (1999), 173-180

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.

January 25, 1999:

SZENES, A.,
[1] Iterated residues and multiple Bernoulli polynomials, Internat. Math. Res. Notices 1998, no. 18, 937-956.

January 13, 1999:

JAKUBEC S.,
[8] Note on Wieferich's congruence for primes $p \equiv 1 \pmod{4}$, Abh. Math. Sem. Univ. Hamburg, 68 (1998), 193-197

SCHIKHOF W.H.,
[1] Ultrametric calculus. An introduction to $p$-adic analysis. Cambridge University Press, Cambridge-New York, 1984. viii+306 pp.

January 7, 1999:

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

SKULA L.,
[18] Fermat and Wilson quotients for $p$-adic integers, Acta Math. Inform. Univ. Ostraviensis, 6 (1998), 167-181.

HOWARD F.T.,
[20] Lacunary recurrences for sums of powers of integers, Fibonacci Quart., 36 (1998), no. 5, 435-442

GLAISHER J.W.L.,
[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.

January 2, 1999:

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.

CRANDALL R.E., DILCHER K., POMERANCE C.,
[1] A search for Wieferich and Wilson primes, Math. Comp., 66 (1997), no. 217, 433-449.

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

GERTSCH A.,
[1] Nombres harmoniques généralisés, C. R. Acad. Sci. Paris Sér. I Math., 324 (1997), no. 1, 7-10.

GIRSTMAIR K.,
[9] Class number factors and distribution of residues, Abh. Math. Sem. Univ. Hamburg, 67 (1997), 65-104.

HACHIMORI Y., ICHIMURA H.,
[1] Semi-local units modulo Gauss sums, Manuscripta Math. 95 (1998), no. 3, 377-395.

[1] An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree $3$, Nagoya Math. J. 146 (1997), 199-223.

KIM JAE MOON,
[2] Class numbers of real quadratic fields, Bull. Austral. Math. Soc., 57 (1998), no. 2, 261-274.

KOLYVAGIN V.A.,
[2] Fermat equations over cyclotomic fields, Proc. Steklov Inst. Math., 208 (1995), 146-165; translation from Tr. Mat. Inst. Steklova, 208 (1995), 163-185.

LE MAOHUA,
[1] A note on the generalized Bernoulli sequences, Ars Combin., 44 (1996), 283-286.

McINTOSH R.J.,
[3] Franel integrals of order four, J. Austral. Math. Soc. Ser. A, 60 (1996), no. 2, 192-203.

MOREE P.,
[2] Primes in arithmetic progression having a prescribed primitive root, MPI für Math., Bonn, Preprint Ser. 1998(57).

PANCHISHKIN A.A.,
[8] Non-archimedean Mellin transform and $p$-adic $L$-functions, Vietnam J. Math., 25 (1997), no.3, 179-202.

SCHOOF R.,
[1] Minus class groups of the fields of the $l$th roots of unity, Math. Comp., 67 (1998), no. 223, 1225-1245.

UENO K., NISHIZAWA M.,
[1] Multiple gamma functions and multiple $q$-gamma functions, Publ. Res. Inst. Math. Sci., 33 (1997), no. 5, 813-838.

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.

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.

POLOVINKIN V. I.,
[1] Approximations of the Bernoulli polynomials by constants and applications to the theory of quadrature formulas, Siberian Adv. Math., 8 (1998), no. 2, 110-121.