# 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.
December 30, 2003:

KIM TAEKYUN,
[8] On $p$-adic $q$-$L$-functions and sums of powers. Discrete Math. 252 (2002), no. 1-3, 179-187.

SLAVUTSKII I.SH.
[36] A real quadratic field and the Ankeny-Artin-Chowla conjecture. (Russian.) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 286 (2002), Anal. Teor. Chisel i Teor. Funkts. 18, 159-168, 230-231.

SUN ZHI-HONG,
[6] Five congruences for primes. Fibonacci Quart. 40 (2002), no. 4, 345-351.

CARLITZ L.,
[106] A note on the generalized Wilson's theorem. Amer. Math. Monthly 71 (1964), 291-293.

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).

DAHLGREN T.,
[1] Sur le théorème de condensation de Cauchy. Dissertation, Lund, 1918. 69pp. (Ch. 1: Sur les nombers et les polynomes de Bernoulli doubles et multiples.)

GLAISHER J.W.L.,
[42] On the series $\frac 1 3 - \frac 1 5 + \frac 1 7 + \frac 1 {11} - \frac 1 {13} - \cdots$. Quart. J. Math. 25 (1891), 375-383

December 29, 2003:

KIM MIN-SOO, KIM TAEKYUN
[5] Bernoulli numbers in $p$-adic analysis. Appl. Math. Comput. 146 (2003), no. 1, 289-297.

DOYON B., LEPOWSKY J., MILAS A.,
Twisted modules for vertex operator algebras and Bernoulli polynomials. Int. Math. Res. Not. 2003, no. 44, 2391-2408.

LUO QIU-MING, GUO TIAN FEN, QI FENG,
[1] Relations of Bernoulli numbers and Euler numbers. (Chinese) J. Henan Norm. Univ. Nat. Sci. 31 (2003), no. 2, 9-11.

LUO QIU MING,
[2] The relations of Bernoulli polynomials and Euler polynomials. (Chinese) Math. Practice Theory 33 (2003), no. 3, 119-122.

NATALINI P., BERNARDINI A.,
[1] A generalization of the Bernoulli polynomials. J. Appl. Math. 2003, no. 3, 155-163.

CHEN HONGWEI,
[1] Bernoulli numbers via determinants. Internat. J. Math. Ed. Sci. Tech. 34 (2003), no. 2, 291-297.

[1] Left factorials, Bernoulli numbers, and the Kurepa conjecture. (Russian) Publ. Inst. Math. (Beograd) (N.S.) 72(86) (2002), 11-22.

LIU JIAN JUN,
[1] A kind of counting identities containing Bernoulli numbers. (Chinese) J. Liaoning Univ. Nat. Sci. 29 (2002), no. 4, 301-303.

SÁNCHEZ-PEREGRINO R.,
[3] A note on a closed formula for Poly-Bernoulli numbers. Amer. Math. Monthly 109 (2002), no. 8, 755-756.

ZHU WEI YI,
[1] An identical relation between the Bernoulli numbers and the Euler numbers. (Chinese) J. Ningxia Univ. Nat. Sci. Ed. 22 (2001), no. 4, 370-371.

BENCZE M., SMARANDACHE F.,
[1] About Bernoulli's numbers. Octogon Math. Mag. 7 (1999), no. 1, 151-153.

LIU GUO DONG,
[9] Recurrent sequences and higher-order multivariable Euler-Bernoulli polynomials. (Chinese) Xiamen Daxue Xuebao Ziran Kexue Ban 38 (1999), no. 3, 352-356.

BECK M.,
[1] Dedekind cotangent sums. Acta Arith. 109 (2003), no. 2, 109-130.

CAI TIAN XIN, GRANVILLE A.,
[1] On the residues of binomial coefficients and their products modulo prime powers. Acta Math. Sin. (Engl. Ser.) 18 (2002), no. 2, 277-288.

ELKIES N. D.,
[1] On the sums $\sum\sp \infty\sb {k=-\infty}(4k+1)\sp {-n}$. Amer. Math. Monthly 110 (2003), no. 7, 561-573.

August 11, 2003:

LUO QIU-MING, QI FENG,
[1] Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials. Adv. Stud. Contemp. Math. (Kyungshang) 7 (2003), no. 1, 11-18.

TSABAN B.,
[1] Bernoulli numbers and the probability of a birthday surprise. Discrete Appl. Math. 127 (2003), no. 3, 657-663.

KANEKO M., KUROKAWA N., WAKAYAMA M.,
[1] A variation of Euler's approach to values of the Riemann zeta-function. Kyushu J. Math. 57 (2003), no. 1, 175-192.

SZENES, A.,
[2] Residue theorem for rational trigonometric sums and Verlinde's formula. Duke Math. J. 118 (2003), no. 2, 189-227.

GUNNELLS P.E., SCZECH R.,
[1] Evaluation of Dedekind sums, Eisenstein cocycles, and special values of $L$-functions. Duke Math. J. 118 (2003), no. 2, 229-260.

FOX, G.J.,
[6] A method of Washington applied to the derivation of a two-variable $p$-adic $L$-function. Pacific J. Math. 209 (2003), no. 1, 31-40.

August 6, 2003:

BYEON D.,
[2] Existence of certain fundamental discriminants and class numbers of real quadratic fields. J. Number Theory 98 (2003), no. 2, 432-437.

CHEN KWANG-WU,
[2] Sums of products of generalized Bernoulli polynomials. Pacific J. Math. 208 (2003), no. 1, 39-52.

CHOI JUNESANG,
[2] Note on Cahen's integral formulas. Commun. Korean Math. Soc. 17 (2002), no. 1, 15-20.

NAGASAKA Y., OTA K., SEKINE C.,
[1] Generalizations of Dedekind sums and their reciprocity laws. Acta Arith. 106 (2003), no. 4, 355-378.

OTA K.,
[2] Dedekind sums with characters and class numbers of imaginary quadratic fields. Acta Arith. 108 (2003), no. 3, 203-215.

[3] Derivatives of Dedekind sums and their reciprocity law. J. Number Theory 98 (2003), no. 2, 280-309.

ZUDILIN W.,
[1] Algebraic relations for multiple zeta values. Russian Math. Surveys 58 (2003), no. 1, 1-20

July 5, 2003:

LUO QIU MING,
[1] Generalizations of Bernoulli numbers and higher-order Bernoulli numbers. (Chinese) Pure Appl. Math. 18 (2002), no. 4, 305-308.

CHEON GI-SANG,
[1] A note on the Bernoulli and Euler polynomials. Appl. Math. Lett. 16 (2003), no. 3, 365-368.

DAMIANOU P., SCHUMER P.,
[1] A theorem involving the denominator of Bernoulli numbers. Math. Mag. 76 (2003), 219-224.

[10] Universal Kummer congruences mod prime powers. Preprint, June 24, 2003.

LIN KE-PAO, YAU STEPHEN S.-T.,
[1] Counting the Number of Integral Points in General n-Dimensional Tetrahedra and Bernoulli Polynomials. Canad. Math. Bull. 46 (2003), no. 2, 229-241.

May 1, 2003:

BYKOVSKII V.A.,
[1] Pairwise products of Eisenstein series, and Manin theta functions. (Russian) Dokl. Akad. Nauk 375 (2000), no. 2, 154-156.

CAI TIANXIN,
[1] A congruence involving the quotients of Euler and its applications. I. Acta Arith. 103 (2002), no. 4, 313-320.

LEU MING-GUANG,
[1] Character sums and the series $L(1,\chi)$. J. Aust. Math. Soc. 70 (2001), no. 3, 425-436.

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.

PORUBSKÝ S.,
[9] Covering systems, Kubert identities and difference equations. Math. Slovaca 50 (2000), no. 4, 381-413.

CHANG KU-YOUNG, KWON SOUN-HI,
[3] Class numbers of imaginary abelian number fields. Proc. Amer. Math. Soc. 128 (2000), no. 9, 2517-2528.

GAMELIN T.W.,
[1] Complex analysis. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2001. xviii+478 pp.

van der POORTEN A.J., te RIELE, H.J.J., WILLIAMS H.C.,
[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.

YOUNG P.T.,
[3] On the behavior of some two-variable $p$-adic $L$-functions. J. Number Theory 98 (2003), no. 1, 67-88.

BÜLOW T.,
[1] The negative Pell equation. C. R. Math. Acad. Sci. Soc. R. Can. 24 (2002), no. 2, 55-60.

SITARAMAN S.,
[2] Note on a Fermat-type Diophantine equation. J. Number Theory 99 (2003), no. 1, 29-35.

LIU GUO DONG,
[8] Higher order multivariable Nörlund Euler-Bernoulli polynomials. Appl. Math. Mech. (English Ed.) 23 (2002), no. 11, 1348-1356; translated from Appl. Math. Mech. 23 (2002), no. 11, 1203-1210 (Chinese).

SUN ZHI-WEI,
[2] General congruences for Bernoulli polynomials. Discrete Math. 262 (2003), no. 1-3, 253-276.

JANG YOUNGHO, KIM DAE SAN,
[1] On higher order generalized Bernoulli numbers. Appl. Math. Comput. 137 (2003), no. 2-3, 387-398.

WAGSTAFF S.S. JR.,
[7] Prime divisors of the Bernoulli and Euler numbers. Number theory for the millennium, III (Urbana, IL, 2000), 357-374, A K Peters, Natick, MA, 2002.

EIE M., ONG Y.L.,
[2] A new approach to congruences of Kummer type for Bernoulli numbers. Number theory for the millennium, I (Urbana, IL, 2000), 377-391, A K Peters, Natick, MA, 2002.

DILCHER K.,
[10] Bernoulli numbers and confluent hypergeometric functions. Number theory for the millennium, I (Urbana, IL, 2000), 343-363, A K Peters, Natick, MA, 2002.

KIM MIN-SOO, SON JIN-WOO
[4] A $q$-analogue of the Dirichlet $L$-function. Algebra Colloq. 9 (2002), no. 4, 469-480.

CHO HAE-SOOK, KIM EUN-SUP,
[1] A note on $q$-analogue of Volkenborn integral. Proceedings of the Jangjeon Mathematical Society, 81-90, Proc. Jangjeon Math. Soc., 4, Jangjeon Math. Soc., Hapcheon, 2002.

KIM YUNG-HWAN, PARK DAL-WON, JANG LEE-CHAE,
[1] A note on $q$-analogue of Volkenborn integral. Adv. Stud. Contemp. Math. (Kyungshang) 4 (2002), no. 2, 159-163.

February 25, 2003:

JANG LEECHAE,
[1] A note on Kummer congruence for the Bernoulli numbers of higher order. Proc. Jangjeon Math. Soc. 5 (2002), no. 2, 141-146.

JANG LEE CHAE, PAK HONG KYUNG,
[1] Non-Archimedean integration associated with $q$-Bernoulli numbers. Proc. Jangjeon Math. Soc. 5 (2002), no. 2, 125-129.

GEKELER E.-U.,
[3] A series of new congruences for Bernoulli numbers and Eisenstein series. J. Number Theory 97 (2002), no. 1, 132-143.

KIM TAEKYUN,
[7] Some formulae for the $q$-Bernoulli and Euler polynomials of higher order. J. Math. Anal. Appl. 273 (2002), no. 1, 236-242.

[1] On $m$th order Bernoulli polynomials of degree $m$ that are Eisenstein. Colloq. Math. 93 (2002), no. 1, 21-26.

FOX, G.J.,
[5] Kummer congruences for expressions involving generalized Bernoulli polynomials. J. Théor. Nombres Bordeaux 14 (2002), no. 1, 187-204.

KARPENKOV O.N.,
[1] Combinatorics of multiboundary singularities of the series $B\sp l\sb n$ and the Bernoulli-Euler numbers. (Russian) Funktsional. Anal. i Prilozhen. 36 (2002), no. 1, 78-81; translation in Funct. Anal. Appl. 36 (2002), no. 1, 65-67.

KELLNER B.,
[1] Über irreguläre Paare höherer Ordnungen. Diplomarbeit, Göttingen, 2002.

COSTABILE F., GUALTIERI M.I., SERRA CAPIZZANO S.,
[1] An iterative method for the computation of the solutions of nonlinear equations. Calcolo 36 (1999), no. 1, 17-34.

BAMBAH R.P.,
[1] Chowla, the mathematics man. Math. Student 67 (1998), no. 1-4, 153-161.