Bernoulli Bibliography

Publications added in 2002


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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.

BOWMAN D., BRADLEY D. M.,
[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.


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