Bernoulli Bibliography

P-Q

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.
J07.0132.01

[2] Relation nouvelle entre les nombres de Bernoulli, Bull. Acad. Royal Belgique, Cl. Sci. (2), 41 (1876), 1017.
J08.0147.02

[3] Sur les nombres de Bernoulli et sur quelques fonctions qui s'y rattachent, Ann. Soc. Sci. Bruxelles, 1B (1876), 43-50.
J08.0147.01

[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.
J11.0187.02

PAK HONG-KYUNG, RIM SEOGH-HOON,
[1] $q$-Bernoulli numbers and polynomials. Proceedings of the Jangjeon Mathematical Society, 31-36, Proc. Jangjeon Math. Soc., 3, Hapcheon, 2001.
M2003b:11131

PAK HONG-KYUNG: see also JANG LEE CHAE, PAK HONG KYUNG, RIM SEOG-HOON, PARK DAL-WON

PAK HONG-KYUNG: see also KIM TAEKYUN, JANG LEE-CHAE, PAK HONG KYUNG

PAK HONG-KYUNG: see also KIM TAEKYUN, JANG LEE CHAE, RIM SEOG-HOON, PAK HONG-KYUNG

PAK HONG-KYUNG: see also JANG LEE CHAE, PAK HONG KYUNG

PAK I. M.: see KUZNETSOV A. G., PAK I. M., POSTNIKOV A. E.

PALAMÀ G.,
[1] Sui numeri di Bernoulli e sui coefficienti delle tangenti. Boll. Unione Mat. Ital. 15 (1936), 126-128

Pan, Hao; Sun, Zhi-Wei,
[1] New identities involving Bernoulli and Euler polynomials. J. Combin. Theory Ser. A 113 (2006), no. 1, 156--175.
M2006j:05020

[2] On $q$-Euler numbers, $q$-Salié numbers and $q$-Carlitz numbers. Acta Arith. 124 (2006), no. 1, 41-57.

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; M2000c:11193

[9] On the Siegel-Eisenstein measure and its applications. Proceedings of the Conference on $p$-adic Aspects of the Theory of Automorphic Representations (Jerusalem, 1998). Israel J. Math. 120 (2000), part B, 467-509.
Z977.11021; M2002a:11054

PANCHISHKIN A.A.: see also MANIN YU.I., PANCHISHKIN A.A.

PANDAY P.: see KHANNA I.K., PANDAY P.

PANDHARIPANDE R.: see FABER C., PANDHARIPANDE R.,

PÁNEK A.,
[1] Das System der Bernoullischen Zahlen, Prag, 1877.

PANJA G.K., DUBE P.P.,
[1] On generalized Bernoulli polynomials. Rev. Bull. Calcutta Math. Soc. 8 (2000), no. 1-2, 43-48.
M2003d:33020

PAP E.,
[1] Complex analysis through examples and exercises. Kluwer Texts in the Mathematical Sciences, 21. Kluwer Academic Publishers Group, Dordrecht, 1999. x+337 pp.
Z0957.30001; M2000m:30001

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

PARK D.W.: see JANG L.C., KIM J.H., KIM T., LEE D.H., PARK D.W., RYOO C.S.

PARK DAL-WON: see JANG LEE-CHAE, KIM TAEKYUN, LEE DEOK-HO, PARK DAL-WON.

PARK DAL-WON: see also JANG LEECHAE, KIM TAEKYUN, PARK DAL-WON.

PARK DAL-WON: A HREF="bernj.html#JAPARIPA">see also JANG LEE CHAE, PAK HONG KYUNG, RIM SEOG-HOON, PARK DAL-WON

PARK DAL-WON: see also KIM YUNG-HWAN, PARK DAL-WON, JANG LEE-CHAE.

Parks, Harold R.,
[1] Sums of non-integral powers. J. Math. Anal. Appl. 297 (2004), no. 1, 343-349.
M2005f:11026

PARODI M.,
[1] Fonction $\zeta$ de Riemann et nombres de Bernoulli, C.R. Acad. Sci., Paris, 240 (1955), 1395-1396.
Z64.06901; 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.
Z144.06604; 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] Sopra i numeri bernoulliani. Rend. Ist. Lomb. (2) 35 (1902),377-389.
J33.0457.02

[2] I determinanti ricorrenti e i nuovi numeri pseudo-Euleriani, Rend Ist Lomb., serie II, 40 (1907), 461-475.
J38.0199.03

[3] I nuovi numeri pseudo-tangenziali, Rend. Palermo, 23 (1907), 358-366.
J38.0466.03

[4] Repertorium der höheren Mathematik, Druck und Verlag von B. G. Teubner Leipzig, 1910.
J41.0044.01; J41.0045.01

PATASHNIK O.: see GRAHAM R.L., KNUTH D.E., PATASHNIK O.

Pathan, M. A.,
[1] Generating functions of the Laguerre-Bernoulli polynomials involving bilateral series. South East Asian J. Math. Math. Sci. 3 (2004), no. 1, 33-38.
Z1063.33011; M2005i:33012

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.
J32.0069.02

Peart, Paul; Woan, Wen-Jin; Tankersley, Barbara,
[1] Algebraic and combinatorial interpretations of the Genocchi triangle. 36th Southeastern International Conference on Combinatorics, Graph Theory, and Computing. Congr. Numer. 175 (2005), 45-51.
M2006h:05018

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.

PERL E.,
[1] Untersuchungen über Differentialkoeffizienten erster und zweiter Art, insbesondere über ihren Zusammenhang mit verwandten Grössen. Diss. Königsberg. 1911, 126 pp. (4. Independente Darstellungen der Bernoullischen Zahlen).
J42.0312.03

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).
J30.0386.03

[2] On the Bernoulli polynomials, Rozpravy II. Trídy Ceské Akad., no. 40, 53 (1943), 16pp., (Czech).
Z63.06175; 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.
J36.0499.01

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.
J55.0131.01

PIERCE T. A.,
[1] Note on Bernoulli's numbers. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 199.
J48.0255.09

PIETROCOLA C.,
[1] Sui numeri e polinomi di Bernoulli, Giorn. mat., Napoli, 34 (1896), 48-72.
J27.0212.01

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; M99a:11040

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

PITMAN J., YOR M.,
[1] Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude. Studia Sci. Math. Hungar. 35 (1999), no. 3-4, 457-474.
Z0973.60082; M2001h:60146

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.

PLATNER G.,
[1] Sul polinomio bernoulliano. Rend. Ist. Lomb. (3) 25 (1892), 1179-1188.
J24.0237.02

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.
Z49.02804; 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.

POKROVSKY P. M.,
[1] The Euler-Maclaurin summation formula and its applications (in Russian). Kiew Univ. No. 12 (1898), 1-14.
J29.0216.01

Polezzi, Marcelo,
[1] Congruences for tangent and Genocchi numbers. JP J. Algebra Number Theory Appl. 6 (2006), no. 1, 111-116.
M2006m:11034

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.
J46.0193.04

[2] Über die irregulären Kreiskörper der $l$-ten und $l^2$-ten Einheitswurzeln, Math. Zeit., 21 (1924), 1-38.
J50.0111.02

[3] Relations entre les dérivées logarithmiques de Kummer et les logarithmes $\pi$-adiques, Bull. Sci. Math., (2), 70 (1946), 199-218.
Z63.06295; M9-273d

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.
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.
Z55.27802; Z55.27803; M15-512a; M15-512b; R1956,5294K

[2] Problems and theorems in analysis. 2 Vols., Springer-Verlag, New York-Berlin, 1972, 1976.
M49#8782; M53#2

POMERANCE C.: see PENNEY D.E., POMERANCE C.

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

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

POMMERSHEIM J.E.: see GAROUFALIDIS S., POMMERSHEIM J.E.,

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

van der POORTEN A.J., te RIELE, H.J.J., WILLIAMS H.C.,
[1] Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than $100\,000\,000\,000$. Math. Comp. 70 (2001), no. 235, 1311-1328.
M2001j:11125

[2] Corrigenda and addition to: "Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than $100\,000\,000\,000$" [Math. Comp. 70 (2001), no. 235, 1311-1328]. Math. Comp. 72 (2003), no. 241, 521-523.
M2003h:11162

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.
Z268.10044; 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.
Z809.11012; 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.
Z948.11012

[8] Identities with covering systems and Appell polynomials. Number theory in progress, Vol. 1 (Zakopane, 1997), 407-417, de Gruyter, Berlin, 1999.
Z934.11009; M2000e:11013; R03.05-13A.156

[9] Covering systems, Kubert identities and difference equations. Math. Slovaca 50 (2000), no. 4, 381-413.
Z0991.11005; M2002h:11013

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

[3] Geometry VI. Riemannian geometry. Translated from the 1998 Russian edition by S. A. Vakhrameev. Encyclopaedia of Mathematical Sciences, 91. Springer-Verlag, Berlin, 2001. xviii+503 pp.
Z0993.53001; M2002g:53001

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.
Z155.02701; M39#1338; R1968,9A140

POUSSIN F.-H.,
[1] Polynômes et nombres d'Euler. Thàse 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.
J54.0230.01

DE PRESLE A.G.V.,
[1] Determination des nombres de Bernoulli, Bull. Soc. Math. France, 14 (1886), 100-103.
J18.0228.01

[2] Dérivées successives d'une puissance entière d'une fonction d'une variable, dérivées successives d'une fonction de fonction et application à la détermination des nombres de Bernoulli. Bull. Soc. Math. France 16 (1888), 157-162.
J20.0266.02

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

[2] Combinatorics of geometrically distributed random variables: new $q$-tangent and $q$-secant numbers. Int. J. Math. Math. Sci. 24 (2000), no. 12, 825-838.
Z0965.05012; M2001h:05017

[3] On Cantor's singular moments. Southwest J. Pure Appl. Math. 2000, no. 1, 27-29 (electronic).
Z0992.11054; M2001e:11126

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), 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.
J58.0160.01

PUTNAM T. M.,
[1] Residues of certain sums of powers of integers. Amer. Math. Monthly, 21 (1914), no. 7, 220-221.
J45.0332.20

QI FENG: see GUO BAI-NI, QI FENG

QI FENG: see also GUO SEN-LIN, QI FENG

QI FENG: see also LUO QIU-MING, QI FENG

QI FENG: A HREF="bernl.html#LUGUQIDE">see also LUO QIU-MING, GUO BAI-NI, QI FENG, DEBNATH L.

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

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