# Bernoulli Bibliography

This file contains, in reverse chronological order, the latest items that have been added to the bibliography. For references to the reviewing journals, see the main bibliography.
November 11, 2002:

BANKS W.,
[1] Some unusual identities for special values of the Riemann zeta function. Ramanujan J. 5 (2001), no. 2, 153-157.

BERG L.,
[1] On the solution of Jordan's system of difference equations. Rostock. Math. Kolloq. No. 56 (2002), 25-28.

[2] On polynomials related with generalized Bernoulli numbers. Rostock. Math. Kolloq. No. 56 (2002), 55-61.

BRETTI G, RICCI P.E.,
[1] Euler polynomials and the related quadrature rule. Georgian Math. J. 8 (2001), no. 3, 447-453.

GUO BAI-NI, QI FENG,
[1] Generalization of Bernoulli polynomials. Internat. J. Math. Ed. Sci. Tech. 33 (2002), no. 3, 428-431.

LIU GUO DONG, LI RONG XIANG,
[1] Sums of products of Euler-Bernoulli-Genocchi numbers. (Chinese) J. Math. Res. Exposition 22 (2002), no. 3, 469-475.

SÁNCHEZ-PEREGRINO R.,
[2] Closed formula for poly-Bernoulli numbers. Fibonacci Quart. 40 (2002), no. 4, 362-364.

SLAVUTSKII I.SH.,
[35] On the generalized Glaisher-Hong's congruences. Chinese Ann. Math. Ser. B 23 (2002), no. 1, 63-66.

SUN QI, HONG SHAO-FANG,
[1] The $p$-adic approach to Wolstenholme's theorem. Northeast. Math. J. 17 (2001), no. 2, 226-230.

SUN ZHI-HONG,
[5] Invariant sequences under binomial transformation. Fibonacci Quart. 39 (2001), no. 4, 324-333.

USTINOV A.V.,
[1] Diskretnyi analog formuly summirovaniya Ejlera [A discrete analogue of Euler's summation formula], Mat. Zametki 71 (2002), no. 6, 931-936.

July 19, 2002:

AGOH T.,
[24] Congruences involving Bernoulli numbers and Fermat-Euler quotients. J. Number Theory, 94 (2002), no. 1, 1-9.

BILU Yu. F., BRINDZA B., KIRSCHENHOFER P., Pintér Á., TICHY R. F.,
[1] Diophantine equations and Bernoulli polynomials. With an appendix by A. Schinzel. Compositio Math. 131 (2002), no. 2, 173-188.

[1] Multiple polylogarithms: a brief survey. In: $q$-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), 71-92, Contemp. Math., 291, Amer. Math. Soc., Providence, RI, 2001.

[1] Swinnerton-Dyer type congruences for certain Eisenstein series. $q$-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), 93-108, Contemp. Math., 291, Amer. Math. Soc., Providence, RI, 2001.

BUNDSCHUH P., JI CHUN-GANG, SHAN ZUN,
[1] A remarkable class of congruences. Acta Sci. Math. (Szeged) 67 (2001), no. 3-4, 493-500.

CHANG CHENG-HUNG, MAYER D.H.
[2] Eigenfunctions of the transfer operators and the period functions for modular groups. Dynamical, spectral, and arithmetic zeta functions (San Antonio, TX, 1999), 1-40, Contemp. Math., 290, Amer. Math. Soc., Providence, RI, 2001.

COOPER S.,
[1] On sums of an even number of squares, and an even number of triangular numbers: an elementary approach based on Ramanujan's ${}\sb 1\psi\sb 1$ summation formula. In: $q$-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), 115-137, Contemp. Math., 291, Amer. Math. Soc., Providence, RI, 2001.

EGAMI S.,
[1] Reciprocity laws of multiple zeta functions and generalized Dedekind sums. In: Analytic number theory and related topics (Tokyo, 1991), 17-27, World Sci. Publishing, River Edge, NJ, 1993.

HOLDEN J.,
[2] Comparison of algorithms to calculate quadratic irregularity of prime numbers. Math. Comp. 71 (2002), no. 238, 863-871.

SHIRATANI K.,
[10] On generalized periods of cusp forms. In: Investigations in number theory, 479-492, Adv. Stud. Pure Math., 13, Academic Press, Boston, MA, 1988.

STOLL M.,
[1] On the arithmetic of the curves $y\sp 2=x\sp l+A$. II. J. Number Theory 93 (2002), no. 2, 183-206.

[4] Special $p$-adic analytic functions and Fourier transforms. J. Number Theory 60 (1996), no. 2, 393-408.

ZHANG WENPENG,
[4] On the general Dedekind sums and one kind identities of Dirichlet $L$-functions. (Chinese. English, Chinese summary) Acta Math. Sinica 44 (2001), no. 2, 269-272.

June 10, 2002:

KIM MIN-SOO, SON JIN-WOO
[2] On a multidimensional Volkenborn integral and higher order Bernoulli numbers. Bull. Austral. Math. Soc. 65 (2002), no. 1, 59-71.

[3] Some remarks on a $q$-analogue of Bernoulli numbers. J. Korean Math. Soc. 39 (2002), no. 2, 221-236.

OTA K.,
[1] On Kummer-type congruences for derivatives of Barnes' multiple Bernoulli polynomials. J. Number Theory 92 (2002), no. 1, 1-36.

COSTABILE F.A., DELL'ACCIO F.,
[2] Expansions over a simplex of real functions by means of Bernoulli polynomials. In memory of W. Gross. Numer. Algorithms 28 (2001), no. 1-4, 63-86.

DILCHER K., MALLOCH L.,
[1] Arithmetic properties of Bernoulli-Padé numbers and polynomials. J. Number Theory 92 (2002), no. 2, 330-347.

ISMAIL M.E.H., RAHMAN, M.,
[1] Inverse operators, $q$-fractional integrals, and $q$-Bernoulli polynomials. J. Approx. Theory 114 (2002), no. 2, 269-307.

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

CHANG CHING-HUA, HA CHUNG-WEI,
[2] On recurrence relations for Bernoulli and Euler numbers. Bull. Austral. Math. Soc. 64 (2001), no. 3, 469-474.

KIM TAEKYUN, RIM SEOG-HOON,
[4] Some $q$-Bernoulli numbers of higher order associated with the $p$-adic $q$-integrals. Indian J. Pure Appl. Math. 32 (2001), no. 10, 1565-1570.

PRODINGER H.,
[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.

February 25, 2002:

BORWEIN J.M., BROADHURST D.J., KAMNITZER J.,
[1] Central binomial sums, multiple Clausen values, and zeta values. Experiment. Math. 10 (2001), no. 1, 25-34.

CHOWLA S.D.,
[3] Some properties of Eulerian numbers. Tohoku Math. J. 30 (1929), 324-327

GRAF J. H.,
[1] Einleitung in die Theorie der Gammafunction und der Euler'schen Integrale. K.J. Wyss, Bern, 1894.

LIU MAI XUE, ZHANG ZHI ZHENG,
[1] A class of computational formulas involving the multiple sum on Genocchi numbers and the Riemann zeta function. (Chinese) J. Math. Res. Exposition 21 (2001), no. 3, 455-458.

KLUYVER J.C.,
[6] Over eenige getallenreeksen van Euler. Versl. Meed. Kon. Ak. Weten., Amsterdam 24 (1916), 1816-1822.

NAGEL T.,
[1] Note sur l'application d'une formule d'inversion de la théorie des nombres. Norsk Matem. Tidsskr. 1 (1919), 40-44.

SCHLÖMILCH O.,
[9] Übungsaufgaben für Schüler. III. Arithmetisches Theorem. Arch. für Math. und Phys., 14 (1850), 108-109.

February 20, 2002:

BALANZARIO E.P.,
[1] Evaluation of Dirichlet Series. Amer. Math. Monthly 108 (2001), no. 10, 9699-971

BERNDT B.C.,
[14] The evaluation of certain classes of nonabsolutely convergent double series. SIAM J. Math. Anal. 6 (1975), no. 6, 966-977.

BROOKE M.,
[1] Fibonacci formulas. Fibonacci Quart. 1 (1963), 60.

FAIRLIE D.B., VESELOV A.P.,
[1] Faulhaber and Bernoulli polynomials and solitons. Advances in nonlinear mathematics and science. Phys. D 152/153 (2001), 47-50.

HOLDEN J.,
[1] Irregularity of prime numbers over real quadratic fields. Algorithmic number theory (Portland, OR, 1998), 454-462, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998.

JANG LEE-CHAE, KIM TAEKYUN, RIM SEOGHOON, SON JIN-WOO,
[1] On the values of $q$-analogue of zeta and $L$-functions. Proceedings of the Jangjeon Mathematical Society, 11-18, Proc. Jangjeon Math. Soc., 1, Jangjeon Math. Soc., Hapcheon, 2000.

KIM TAEKYUN, JANG LEE-CHAE, PAK HONG KYUNG,
[1] A note on $q$-Euler and Genocchi numbers. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 8, 139-141.

KNOLL, F.,
[1] Die zyklischen Funktionen und die damit zusammenhängenden linearen Operationen. Verallgemeinerte Bernoullische Polynome. Deutsche Math. 1 (1936), 156-162.

KNOPFMACHER A., ROBBINS N.,
[1] Some arithmetic properties of Eulerian numbers. J. Combin. Math. Combin. Comput. 36 (2001), 31-42.

LIU GUO DONG,
[6] Identities and congruences involving higher-order Euler-Bernoulli numbers and polynomials. Fibonacci Quart. 39 (2001), no. 3, 279-284.

[7] Computational formulas for Euler-Bernoulli polynomials of $n$ variables. (Chinese. English summary) J. Wuhan Univ., Nat. Sci. Ed. 44 (1998), no.5, 554-556.

MURTY M. RAM, REECE M.,
[1] A simple derivation of $\zeta(1-K)=-B\sb K/K$. Funct. Approx. Comment. Math. 28 (2000), 141-154.

RAMARÉ, O.,
[1] Approximate formulae for $L(1,\chi)$. Acta Arith. 100 (2001), no. 3, 245-266.

RZUDKOWSKI G.,
[1] Euler-Maclaurin summation and the generalized factorial. Math. Gazette 85 (2001), no. 504, 507-512.

SATOH J.,
[7] Another look at the $q$-analogue from the viewpoint of formal groups. Proceedings of the Jangjeon Mathematical Society, 145-159, Proc. Jangjeon Math. Soc., 1, Jangjeon Math. Soc., Hapcheon, 2000.

SCHNEIDER I.,
[1] Potenzsummenformeln im 17. Jahrhundert. Historia Math. 10 (1983), no. 3, 286-296.

TUENTER H.J.H.,
[1] On the sums $\sum_{i=1}^n\Lceil i/p \Rceil^m$ and $\sum_{i=1}^n \Lfloor i/p \Rfloor^m$}, Pi Mu Epsilon Journal 11 (2000), no. 2, 97-99.

WALSTRA, K.W.,
[1] Sur les fonctions de Lubbock. Nieuw Arch. Wisk. (2) 12 (1917), 161-168

ZHANG SHANJIE, JIN JIANMING,
[1] Computation of special functions. John Wiley & Sons, Inc., New York, 1996. xxvi+717 pp. ISBN 0-471-11963-6

February 15, 2002:

CHEN KWANG-WU,
[1] Algorithms for Bernoulli numbers and Euler numbers. J. Integer Seq. 4 (2001), no. 1, Article 01.1.6, 7 pp. (electronic).

CHEN KWANG-WU, EIE MINKING,
[1] A note on generalized Bernoulli numbers. Pacific J. Math. 199 (2001), no. 1, 41-59.

COSTABILE F.A., DELL'ACCIO F.,
[1] Expansion over a rectangle of real functions in Bernoulli polynomials and applications. BIT 41 (2001), no. 3, 451-464.

JANG YOUNGHO, KIM HOIL,
[1] A series whose terms are products of two $q$-Bernoulli numbers in the $p$-adic case. Houston J. Math. 27 (2001), no. 3, 495-510.

LIU GUO DONG,
[5] The generalized central factorial numbers and higher order Nörlund Euler-Bernoulli polynomials. (Chinese). Acta Math. Sinica 44 (2001), no. 5, 933-946.

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.

January 28, 2002:

FUCHS P.,
[1] Bernoulli numbers and binary trees. Tatra Mt. Math. Publ. 20 (2000), 111-117.

JAKUBEC S.,
[12] Remark on certain sums concerning class number. Abh. Math. Sem. Univ. Hamburg, 71 (2001), 69-76.

NARKIEWICZ W.,
[3] The development of prime number theory. From Euclid to Hardy and Littlewood. Springer-Verlag, Berlin, 2000. xii+448 pp.

SÁNDOR J.,
[2] On the open problems OQ.487 and OQ.507, Octogon Math. Mag. 9 (2001), no.1, 550-551; 558-559.

SCHUSTER W.,
[1] Improving Stirling's formula. Arch. Math. (Basel) 77 (2001), no. 2, 170-176.

SRIVASTAVA H.M., TSUMURA H.,
[1] A certain class of rapidly convergent series representations for $\zeta(2n+1)$. J. Comput. Appl. Math. 118 (2000), no. 1-2, 323-335.
[2] Certain classes of rapidly convergent series representations for $L(2n,\chi)$ and $L(2n+1,\chi)$. Acta Arith. 100 (2001), no. 2, 195-201.

YOUNG P.T.,
[2] Kummer congruences for values of Bernoulli and Euler polynomials. Acta Arith. 99 (2001), no. 3, 277-288.

January 10, 2002:

CHANG CHENG-HUNG, MAYER D.H.,
[1] The transfer operator approach to Selberg's zeta function and modular and Maass wave forms for ${\rm PSL}(2,Z)$. In: Emerging applications of number theory (Minneapolis, MN, 1996), 73-141, IMA Vol. Math. Appl., 109, Springer, New York, 1999.

KANEMITSU S., KUZUMAKI T.,
[2] On a generalization of the Maillet determinant. II. Acta Arith. 99 (2001), no. 4, 343-361.

KIM TAEKYUN,
[6] Remark on $p$-adic $q$-$L$-functions and sums of powers. Proc. Jangjeon Math. Soc. 1 (2000), 161-169.

KUCERA R.,
[1] Formulae for the relative class number of an imaginary abelian field in the form of a determinant. Nagoya Math. J. 163 (2001), 167-191.