# Bernoulli Bibliography

This file contains, in reverse chronological order, all items that were added to the bibliography in 2000. For references to the reviewing journals, see the main bibliography.
December 14, 2000:

KATO K., KUROKAWA N., SAITO T.,
[1] Number theory. 1. Fermat's dream. Translations of Mathematical Monographs, 186. Iwanami Series in Modern Mathematics. American Mathematical Society, Providence, RI, 2000. xvi+154 pp.

[1] Power series and asymptotic series associated with the Lerch zeta-function. Proc. Japan Acad. Ser. A Math. Sci. 74 (1998), no. 10, 167-170.

[2] Rapidly convergent series representations for $\zeta(2n+1)$ and their $\chi$-analogue. Acta Arith. 90 (1999), no. 1, 79-89.

KLEINER I.,
[1] From Fermat to Wiles: Fermat's last theorem becomes a theorem. Elem. Math. 55 (2000), no. 1, 19-37.

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.

PORUBSKÝ S.,
[8] Identities with covering systems and Appell polynomials. Number theory in progress, Vol. 1 (Zakopane, 1997), 407-417, de Gruyter, Berlin, 1999.

TENENBAUM G.,
[1] Introduction to analytic and probabilistic number theory. Translated from the second French edition (1995) by C. B. Thomas. Cambridge Studies in Advanced Mathematics, 46. Cambridge University Press, Cambridge, 1995. xvi+448 pp. ISBN: 0-521-41261-7

TAYA H.,
[1] Iwasawa invariants and class numbers of quadratic fields for the prime $3$. Proc. Amer. Math. Soc. 128 (2000), no. 5, 1285-1292.

URBANOWICZ J., WILLIAMS K.S.,
[1] Congruences for $L$-functions. Mathematics and its Applications, 511. Kluwer Academic Publishers, Dordrecht, 2000. xii+256 pp. ISBN: 0-7923-6379-5

December 13, 2000:

KIM TAEKYUN, RIM SEOG-HOON,
[1] A note on $p$-adic Carlitz's $q$-Bernoulli numbers. Bull. Austral. Math. Soc. 62 (2000), no. 2, 227-234.

[2] Generalized Carlitz's $q$-Bernoulli numbers in the $p$-adic number field. Adv. Stud. Contemp. Math. (Pusan) 2 (2000), 9-19.

SUN ZHI-HONG,
[3] Congruences concerning Bernoulli numbers and Bernoulli polynomials. Discrete Appl. Math. 105 (2000), no. 1-3, 193-223.

KUDO A.,
[7] A congruence of generalized Bernoulli number for the character of the first kind. Adv. Stud. Contemp. Math. (Pusan) 2 (2000), 1-8.

WANG YUN KUI, MA WU YU
[1] Necessary and sufficient conditions for Bernoulli's numbers and discriminant prime numbers. (Chinese) J. Huaqiao Univ. Nat. Sci. Ed. 21 (2000), no. 3, 234-238.

[8] Universal higher order Bernoulli numbers and Kummer and related congruences. J. Number Theory 84 (2000), no. 1, 119-135.

SLAVUTSKII I.SH.,
[32] A remark on the paper of A. Simalarides: "Congruences mod $p\sp n$ for the Bernoulli numbers" [Fibonacci Quart. 36 (1998), no. 3, 276-281]. Fibonacci Quart. 38 (2000), no. 4, 339-341.

DATTOLI G., LORENZUTTA S., CESARANO C.,
[1] Finite sums and generalized forms of Bernoulli polynomials. Rend. Mat. Appl. (7) 19 (1999), no. 3, 385-391 (2000).

LIU GUO DONG,
[4] Recurrence sequences and higher order multivariable Euler-Bernoulli polynomials. (Chinese) Numer. Math. J. Chinese Univ. 22 (2000), no. 1, 70-74.

KIM MIN-SOO, SON JIN-WOO,
[1] On Bernoulli numbers. J. Korean Math. Soc. 37 (2000), no. 3, 391-410.

EHRENBORG R., STEINGRIMSSON E.,
[1] Yet another triangle for the Genocchi numbers. European J. Combin. 21 (2000), no. 5, 593-600.

GUO SEN-LIN, QI FENG,
[1] Recursion formulae for $\sum\sp n\sb {m=1}m\sp k$. Z. Anal. Anwendungen 18 (1999), no. 4, 1123-1130.

[4] On the limits of $p$-adic sequences of averages. Sci. Rep. Fac. Ed. Gifu Univ. Natur. Sci. 24 (2000), no. 2, 7-13.

JEDELSKÝ D., SKULA L.,
[1] Some results from the tables of irregularity index of a prime. Acta Math. Inform. Univ. Ostraviensis 8 (2000), 45-50.

FOX G.J., URBANOWICZ J., WILLIAMS K.S.,
[1] Gauss' congruence from Dirichlet's class number formula and generalizations.Number theory in progress, Vol. 2 (Zakopane, 1997), 813-839, de Gruyter, Berlin, 1999.

ZIA-UD-DIN M.,
[2] Some more formulae for the Bernoullian mumbers. Math. Student 15 (1938), 81-157.

October 6, 2000:

JONES G.A., JONES J.M.,
[1] Elementary number theory. Springer-Verlag London, Ltd., London, 1998. xiv+301 pp.

KANEKO M., ZAGIER D.,
[1] Supersingular $j$-invariants, hypergeometric series, and Atkin's orthogonal polynomials. Computational perspectives on number theory (Chicago, IL, 1995), 97-126, AMS/IP Stud. Adv. Math., 7, Amer. Math. Soc., Providence, RI, 1998.

September 7, 2000:

SIACCI F.,
[1] Sull'uso dei determinanti delle potenze intere dei numeri naturala, Annali di Matematica, Ser. I., 7 (1865), 19-24.

SCHOENBERG I.J.,
[1] Monosplines and quadrature formulae. 1969 Theory and Applications of Spline Functions (Proceedings of Seminar, Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1968) pp. 157-207 Academic Press, New York.

[5] Cardinal spline interpolation and the exponential Euler splines. Functional analysis and its applications (Internat. Conf., Eleventh Anniversary of Matscience, Madras, 1973; dedicated to Alladi Ramakrishnan), pp. 477--489. Lecture Notes in Math., Vol. 399, Springer, Berlin, 1974.

STEFFENSEN J.F.,
[2] The poweroid, an extension of the mathematical notion of power. Acta Math. 73 (1941), 333-366.

[3] On the polynomials $R\sb \nu\sp {[\lambda]}(x)$, $N\sb \nu\sp {[\lambda]}(x)$ and $M\sb \nu\sp {[\lambda]}(x)$. Acta Math. 78 (1946), 291-314.

DILCHER K.,
[9] Von Staudt-Clausen Theorem. Encyclopedia of Mathematics, Supplement II. Kluwer Academic Publishers, Dordrecht, 2000.

September 3, 2000:

AGOH T.,
[23] Generalization of Lehmer's congruences for Bernoulli numbers, C. R. Math. Rep. Acad. Sci. Canada 22 (2000), no. 2, 61-65.

KIM MIN-SOO,
[1] On Bernoulli numbers. J. Korean Math. Soc. 37 (2000), no. 3, 391-410.

MUSÈS C.,
[4] Some new considerations on the Bernoulli numbers, the factorial function, and Riemann's zeta function. Appl. Math. Comput. 113 (2000), no. 1, 1-21.

SRIVASTAVA H.M.,
[2] Some formulas for the Bernoulli and Euler polynomials at rational arguments. Math. Proc. Cambridge Philos. Soc. 129 (2000), no. 1, 77-84.

LUCAS, E.,
[7] Sur les sommes des puissances semblables des nombres entries. Nouv. Ann. (2) 16 (1877), 18-26.

MAMBRIANI A.,
[1] Sugli sviluppi, dati dallo Schwatt, di $\sec^p x$ e $\tg^p x$. (Italian) Boll. Unione Mat. Ital. 10 (1931), 17-20.

July 10, 2000:

AGOH T.,
[22] Recurrences for Bernoulli and Euler polynomials and numbers, Exposition. Math. 18 (2000), 197-214.

JANKOVIC Z.,
[1] Summen der gleichen Potenzen der natürlichen Zahlen, Zeitschrift für math. u. naturwiss. Unterricht 74 (1943), 41-44.

KARST E.,
[1] On the coefficients of $\sum_{x=1}^n x^k/\sum_{x=1}^n x^m$, written in terms of n, Pi Mu Epsilon J. 4 (1964), 11-14.

GOULD H.W.,
[1] Stirling number representation problems. Proc. Amer. Math. Soc. 11 (1960), no. 3, 447-451.

[2] The Lagrange interpolation formula and Stirling numbers. Proc. Amer. Math. Soc. 11 (1960), no. 3, 421-425.

[3] The $q$-Stirling numbers of first and second kinds. Duke Math. J. 28 (1961), no. 2, 281-289.

[4] Note on a paper of Klamkin concerning Stirling numbers. Amer. Math. Monthly 68 (1961), no. 5, 477-479.

[10] Evaluation of sums of convolved powers using Stirling and Eulerian numbers.Fibonacci Quart. 16 (1978), no. 6, 488-497, 560-561.

KLAMKIN M.S.,
[1] On a generalization of the geometric series. Amer. Math. Monthly 64 (1957), no. 2, 91-93.

July 8, 2000:

WANG YUN KUI,
[1] General expressions for sums of equal powers and Bernoulli numbers. (Chinese. English, Chinese summary) J. Guangxi Univ. Nat. Sci. Ed. 24 (1999), no. 4, 318-320.

KIM TAEKYUN,
[3] On $p$-adic $q$-Bernoulli numbers. J. Korean Math. Soc. 37 (2000), no. 1, 21-30.

FRAPPIER C.,
[2] Generalised Bernoulli polynomials and series. Bull. Austral. Math. Soc. 61 (2000), no. 2, 289-304.

SATOH J.,
[6] A recurrence formula for $q$-Bernoulli numbers attached to formal group. Nagoya Math. J. 157 (2000), 93-101.

CHEN MING-PO,
[1] An elementary evaluation of $\zeta (2m)$. Chinese J. Math. 3 (1975), no. 1, 11-15.

MEYER J.L.,
[1] Character analogues of Dedekind sums and transformations of analytic Eisenstein series. Pacific J. Math. 194 (2000), no. 1, 137-164.

April 11, 2000:

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

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

CARLITZ L.,
[105] Generating functions, Fibonacci Quart. 7 (1969), no. 4, 359-393.

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

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

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

GRAS G.,
[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.

GREENBERG R.,
[3] On the Jacobian variety of some algebraic curves, Compositio Math. 42 (1980/81), no. 3, 345-359.

HONG SHAOFANG,
[1] Notes on Glaisher's congruences, Chinese Ann. Math. Ser. B 21 (2000), no. 1, 33-38.

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.

KANEMITSU S., KUZUMAKI T.,
[1] On a generalization of the Maillet determinant. Number theory (Eger, 1996), 271-287, de Gruyter, Berlin, 1998.

[3] Rapidly convergent series representations for $\zeta(2n+1)$ and their $\chi$ -analogue, Acta Arith. 90 (1999), no. 1, 79-89.

[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.

KIM JAE MOON,
[3] Units and cyclotomic units in ${Z}\sb p$-extensions, Nagoya Math. J. 140 (1995), 101-116.

SCHMIDT P.,
[1] The Stickelberger element of an imaginary quadratic field, Acta Math. 91 (1999), no. 2, 165-169.

SHOKROLLAHI M.A.,
[2] Relative class number of imaginary abelian fields of prime conductor below 10000, Math. Comp. 68 (1999), no. 228, 1717-1728.

SOULÉ CH.,
[2] Perfect forms and the Vandiver conjecture, J. Reine Angew. Math. 517 (1999), 209-221.

UZBANSKIJ V.M.,
[1] Dmitrij Grave i ego vremya [Dmitrij Grave and his time], Naukova Dumka, Kiev, 1998, 268 pp.

March 31, 2000:

LIU GUO DONG,
[3] Generalized Euler-Bernoulli polynomials of order $n$. (Chinese), Math. Practice Theory 29 (1999), no. 3, 5-10.

SLAVUTSKII I.SH.,
[31] Leudesdorf's theorem and Bernoulli numbers, Arch. Math. (Brno) 35 (1999), 299-303.

SUBRAMANIAN P.R.,
[2] Evaluation of ${\rm Tr}(J\sp {2p}\sb \lambda)$ using the Brillouin function, J. Phys. A, 19 (1986), no. 7, 1179-1187.

[3] Generating functions for angular momentum traces, J. Phys. A, 19 (1986), no. 13, 2667-2670.

SUBRAMANIAN P.R., DEVANATHAN V.,
[2] Recurrence relations for angular momentum traces, J. Phys. A, 13 (1980), 2689-2693.

March 10, 2000:

ROBBINS N.,
[1] Revisiting an old favourite: $\zeta(2m)$, Math. Mag. 72 (1999), no. 4, 317-319.

SCHOENBERG I.J.,
[1] Norm inequalities for a certain class of $C\sp{\infty }$ functions, Israel J. Math. 10 (1971), 364-372.

[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.

[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.

LEE JUNGSEOB,
[1] Integrals of Bernoulli polynomials and series of zeta function, Commun. Korean Math. Soc. 14 (1999), no. 4, 707-716.

LÓPEZ J.L.; TEMME N.M.,
[2] Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials, J. Math. Anal. Appl. 239 (1999), no. 2, 457-477.

January 22, 2000:

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

SLAVUTSKII I.SH.,
[30] About von Staudt congruences for Bernoulli numbers, Comment. Math. Univ. St. Paul. 48 (1999), no. 2, 137-144.

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.

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

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.

January 21, 2000:

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

BERNDT B.C.,
[12] Ramanujan's notebooks. Part IV. Springer-Verlag, New York, 1994. xii+451pp.

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

IBUKIYAMA T.,
[1] On some elementary character sums, Comment. Math. Univ. St. Paul. 47 (1998), no. 1, 7-13.

JAKUBEC S.,
[9] Note on the congruence of Ankeny-Artin-Chowla type modulo $p\sp 2$, Acta Arith. 85 (1998), no. 4, 377-388.

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.

ONO K.,
[1] Indivisibility of class numbers of real quadratic fields, Compositio Math. 119 (1999), no. 1, 1-11.

ROTA G.-C.,
[1] Combinatorial snapshots, Math. Intelligencer 21 (1999), no. 2, 8-14.

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.

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.