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ANGLÈS B.,
[2] Units and norm residue symbol. Acta Arith. 98 (2001), no. 1, 33-51.

BUHLER J.P., CRANDALL R.E., ERNVALL R., METSÄNKYLÄ T., SHOKROLLAHI M. A.,
[1] Irregular primes and cyclotomic invariants to 12 million. Computational algebra and number theory (Milwaukee, WI, 1996). J. Symbolic Comput. 31 (2001), no. 1-2, 89-96.

CRANDALL R.E., POMERANCE C.,
[1] Prime numbers. A computational perspective. Springer-Verlag, New York, 2001. xvi+545 pp.

DRYANOV D., KOUNCHEV O.,
[2] Multivariate Bernoulli functions and polyharmonically exact cubature formula of Euler-Maclaurin. Math. Nachr. 226 (2001), 65-83.

LEMMERMEYER F.,
[1] Reciprocity laws. From Euler to Eisenstein. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2000. xx+487 pp.

MOMIYAMA H.,
[1] A new recurrence formula for Bernoulli numbers. Fibonacci Quart. 39 (2001), no. 3, 285-288.

MURTY M. RAM,
[1] Problems in analytic number theory. Graduate Texts in Mathematics, 206. Readings in Mathematics. Springer-Verlag, New York, 2001. xvi+452 pp.

PANCHISHKIN A.A.,
[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.

POSTNIKOV M. M.,
[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.

RIBENBOIM P.,
[19] Classical theory of algebraic numbers. Universitext. Springer-Verlag, New York, 2001. xxiv+681 pp.

[20] My numbers, my friends. Popular lectures on number theory. Springer-Verlag, New York, 2000. xii+375 pp.

ROSEN K.H. (Editor-in-Chief),
[1] Handbook of discrete and combinatorial mathematics. CRC Press, Boca Raton, FL, 2000. xiv+1232 pp.

SHIRAI S., SATO K.,
[1] Some identities involving Bernoulli and Stirling numbers. J. Number Theory 90 (2001), no. 1, 130-142.

SLAVUTSKII I.SH.,
[34] Partial sums of the harmonic series, $p$-adic $L$-functions and Bernoulli numbers. Number theory (Liptovský Ján, 1999). Tatra Mt. Math. Publ. 20 (2000), 11-17.

TSUJI T.,
[1] Greenberg's conjecture for Dirichlet characters of order divisible by $p$. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 4, 52-54.

August 16, 2001:

The following "new" entries are from H.S. Vandiver's unpublished bibliography VANDIVER [56] which was found and kindly sent to us by Jeff Lagarias. More of these entries to follow in the next update.

d'ALMEIDA AREZ, J. B.,
[1] Duas classes de numeros. Jornal de Scienzias Mathematicas e Astronomicas 15 (1901), 3-24.

BEAUPAIN J.,
[1] Sur une classe de fonctions qui se rattachent aux fonctions de Jacques Bernoulli. Mémoires Couronnés et Mémoires des Savants Étrangers publiés par l'Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Bruxelles, 59 (1901), pt. 1, 33 pp.

BERG F.J. van den,
[3] Nogmaals over de Bernoulliaansche coëfficienten. Amst. Versl. en Meded. (3) 6 (1889), 265-276.

DERUYTS J.,
[1] Rapport sur un Mémoire de M. Beaupain intitulé: ``Sur une classe de fonctions qui se rattachent aux fonctions de Jacques Bernoulli.'' Belg. Bull. Sciences (1900), 255-257.

DICKSON J.D.H.,
[1] On Raabe's Bernoullians. Proc. London Math. Soc. 20 (1889), 14-21.

FEINLER F.J.,
[3] A reduced Bernoulli polynomial and its properties (Abstract). Bull. Amer. Math. Soc., 34 (1928), 698.

GLAISHER J.W.L.,
[20] General summation-formulae in finite differences. Quart. J. Pure Appl. Math., 29 (1898), 303-328.

[25] On a set of coefficients analogous to the Eulerian numbers. Proc. London Math. Soc., 31 (1899), 216-235.

LIPSCHITZ R.,
[2] Sur la fonction de Jacob Bernoulli et sur l'interpolation. C. R. Acad. Sci., Paris, 86 (1878), 119-121.

LUCAS E.,
[1] De quelques nouvelles formules de sommation. Nouv. Ann. Math. (2), 14 (1875), 487-494. [9] Recherches sur plusieurs ouvrages de Léonard de Pise et sur diverses questions d'arithmétique supérieure. Boncompagni Bull. 10 (1877), 129-193, 239-293.

MANDL M.,
[1] Ueber die Summirung einiger Reihen. Sitzungsber. Math.-Natur. Kl. Akad. Wiss., Wien, 94 (1886), 947-955.

NIELSEN N.,
[1] Note sur les séries de fonctions bernoulliennes. Math. Ann. 59 (1904), 103-109.

[19] Note sur une généralisation des nombres d'Euler. Nyt Tidskr. Mat., 27 B (1916), 21-27.

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

PASCAL E.,
[1] Sopra i numeri bernoulliani. Rend. Ist. Lomb. (2) 35 (1902),377-389.

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

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

DE PRESLE A.G.V.,
[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.

SCHIKORE K.,
[1] Die Bernoullischen Zahlen. Published by the author, Breslau, 1929. 1 p.

STERN M.A.,
[4] Verallgemeinerung einer Jacobi'schen Formel. J. Reine Angew. Math., 84 (1877), 216-219.

VANDIVER H.S.,
[56] Bibliography of Articles on Bernoulli and Euler Numbers for the Years 1869-1940. 22 pp., Center for American History, University of Texas at Austin (unpublished).

WIRTINGER W.,
[1] Einige Anwendungen der Euler-Maclaurinschen Summenformel, insbesondere auf eine Aufgabe von Abel. Acta Math. 26 (1902), 255-272.

August 7, 2001:

ARAKAWA T., IBUKIYAMA T., KANEKO M.,
[1] Bernoulli numbers and zeta functions (in Japanese). Makino Shoten Ltd., 2001. ix + 244 pp.

BRIOSCHI F.,
[1] Sulle funzioni Bernoulliane ed Euleriane. Annali di Matematica Pura et Applicata, 1 (1858), 260-263.

SCHLÖMILCH O.,
[5] Uebungsaufgaben für Schüler. Arch. für Math. und Phys., 10 (1847), 340-341.

July 30, 2001:

ADELBERG A.,
[9] Kummer congruences for universal Bernoulli numbers and related congruences for poly-Bernoulli numbers. Int. Math. J. 1 (2002), no. 1, 53-63.

AKIYAMA S., EGAMI S., TANIGAWA Y.,
[1] Analytic continuation of multiple zeta-functions and their values at non-positive integers. Acta Arith. 98 (2001), no. 2, 107-116.

CHANG CHING-HUA, HA CHUNG-WEI,
[2] The imaginary abelian number fields with class numbers equal to their genus class numbers. Colloque International de Théorie des Nombres (Talence, 1999). J. Théor. Nombres Bordeaux 12 (2000), no. 2, 349-365.

CHU WENCHANG,
[1] Symmetric functions and the Riemann zeta series. Indian J. Pure Appl. Math. 31 (2000), no. 12, 1677-1689.

GIRSTMAIR K.,
[10] Cyclotomic matrices and a limit formula for $h\sp -\sb p$. Acta Arith. 97 (2001), no. 2, 129-155.

KIM TAEKYUN,
[3] On a $q$-analogue of the $p$-adic log gamma functions and related integrals. J. Number Theory 76 (1999), no. 2, 320-329.

LEPKA K.,
[1] Matyás Lerch's work on number theory. Masaryk University, Faculty of Science, Brno, 1995. 78 pp.

MATSUOKA Y.,
[1] On the values of the Riemann zeta function at half integers. Tokyo J. Math. 2> (1979), no. 2, 371-377.

NIRENBERG M.,
[1] Cuspidal groups, ordinary Eisenstein series, and Kubota-Leopoldt $p$-adic $L$-functions. Acta Arith. 97 (2001), no. 1, 1-40.

OKADA S.,
[3] A calculus of Bernoulli numbers for function fields. Mem. Gifu Nat. Coll. Technol. (2000), no. 35, 1-4.

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.

SÁNCHEZ-PEREGRINO R.,
[1] The Lucas congruence for Stirling numbers of the second kind. Acta Arith. 94 (2000), no. 1, 41-52.

SON JIN-WOO, JANG DOUK SOO,
[1] A $q$-analogue of $w$-Bernoulli numbers and their applications. Bull. Korean Math. Soc. 38 (2001), no. 2, 399-412.

SUN ZHI-WEI,
[1] Products of binomial coefficients modulo $p\sp 2$. Acta Arith. 97 (2001), no. 1, 87-98.

TOYOIZUMI M.,
[1] Formulae for the Riemann zeta function at half integers. Tokyo J. Math. 3 (1980), no. 1, 177-186.

[2] Formulae for the values of zeta and $L$-functions at half integers. Tokyo J. Math. 4 (1981), no. 1, 193-201.

June 12, 2001:

BYEON D.,
[1] Special values of zeta functions of the simplest cubic fields and their applications. Proc. Japan Acad. Ser. A Math. Sci. 74 (1998), no. 1, 13-15.

CHANG CHING-HUA, HA CHUNG-WEI,
[1] The Green functions of some boundary value problems via the Bernoulli and Euler polynomials. Arch. Math. (Basel) 76 (2001), no. 5, 360-365.

FOX, G.J.,
[4] A $p$-adic $L$-function of two variables. Enseign. Math. (2) 46 (2000), no. 3-4, 225-278.

FRAPPIER C.,
[3] A unified calculus using the generalized Bernoulli polynomials. J. Approx. Theory 109 (2001), no. 2, 279-313.

KIM MIN-SOO, KIM TAEKYUN
[1] An explicit formula on the generalized Bernoulli number with order $n$. Indian J. Pure Appl. Math. 31 (2000), no. 11, 1455-1461.

KIM TAEKYUN,
[4] Sums of products of $q$-Bernoulli numbers. Arch. Math. (Basel) 76 (2001), no. 3, 190-195.

LIBRI G.,
[1] Mémoire sur quelques formules générales d'analyse. J. Reine Angew. Math. 7 (1831), 57-67.

D'OCAGNE M.,
[1] Sur une classe de nombres remarquables. American J. Math. 9 (1887), no. 4, 353-380.

ROTHE H.A.,
[1] Relationen der Lokalausdrücke von Potenzen besonderer merkwürdiger Reihen. In: K. F. Hindernburg, Sammlung combinatorisch-analytischer Abhandlungen, 2-te Sammlung, G. Fleischer, Leipzig, 1800.

SUN ZHI-HONG,
[1] The combinatorial sum $\sum\sb {k\equiv r\pmod m}\binom nk$ and its applications in number theory. III. (Chinese. English, Chinese summary) Nanjing Daxue Xuebao Shuxue Bannian Kan 12 (1995), no. 1, 90-102.

SURY B.,
[2] Values of Euler polynomials. C. R. Math. Acad. Sci. Soc. R. Can. 23 (2001), no. 1, 12-15.

TABIRCA S.,
[1] Some remarks concerning the Bernoulli numbers. Notes Number Theory Discrete Math. 6 (2000), no. 2, 29-33.

April 12, 2001:

ANGLÈS B.,
[1] On the orthogonal of cyclotomic units in positive characteristic. J. Number Theory 79 (1999), no. 2, 258-283.

BÖCHERER S., SCHMIDT C.-G.,
[1] $p$-adic measures attached to Siegel modular forms. Ann. Inst. Fourier (Grenoble) 50 (2000), no. 5, 1375-1443.

DARMON H., DIAMOND F., TAYLOR R.,
[1] Fermat's last theorem. Elliptic curves, modular forms & Fermat's last theorem (Hong Kong, 1993), 2-140, Internat. Press, Cambridge, MA, 1997.

DI BUCCHIANICO A., LOEB D.,
[1] A selected survey of umbral calculus. Electron. J. Combin. 2 (1995), Dynamic Survey 3, 28 pp. (electronic).

DI BUCCHIANICO A., LOEB D., ROTA G.-C.
[1] Umbral calculus in Hilbert space. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 213-238, Progr. Math., 161, Birkhäuser Boston, Boston, MA, 1998.
DUMMIGAN N.,
[1] Period ratios of modular forms. Math. Ann. 318 (2000), no. 3, 621-636.

FABER C., PANDHARIPANDE R.,
[1] Logarithmic series and Hodge integrals in the tautological ring. Michigan Math. J. 48 (2000), 215-252.

GAROUFALIDIS S., POMMERSHEIM J.E.,
[1] Values of zeta functions at negative integers, Dedekind sums and toric geometry. J. Amer. Math. Soc. 14 (2001), no. 1, 1-23.

JAKUBEC S.,
[10] Congruence of Ankeny-Artin-Chowla type for cyclic fields. Math. Slovaca 48 (1998), no. 3, 323-326.

[11] Connection between Schinzel's conjecture and divisibility of the class number $h\sp +\sb p$. Acta Arith. 94 (2000), no. 2, 161-171.

KANOU N.,
[1] Transcendency of zeros of Eisenstein series. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 5, 51-54.

MOLLIN R.A.,
[1] Algebraic number theory. Chapman & Hall/CRC, Boca Raton, FL, 1999. xiv+483 pp.

MOLTENI G.,
[1] Some arithmetical properties of the generating power series for the sequence {z(2k+1)}, Acta Math. Hungar. 90 (2001), no. 1-2, 133-140.

NAGAOKA S.,
[3] A remark on Serre's example of $p$-adic Eisenstein series. Math. Z. 235 (2000), no. 2, 227-250.

RUIJSENAARS S.N.M.,
[1] On Barnes' Multiple Zeta and Gamma Functions. Adv. Math. 156 (2000), no. 1, 107-132.

RAY N.,
[3] Universal constructions in umbral calculus. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 343-357, Progr. Math., 161, Birkhäuser Boston, Boston, MA, 1998.

ROBERT A.M.,
[2] A course in $p$-adic analysis. Graduate Texts in Mathematics, 198. Springer-Verlag, New York, 2000. xvi+437 pp.

SLAVUTSKII I.SH.,
[33] On the generalized Bernoulli numbers that belong to unequal characters. Rev. Mat. Iberoamericana 16 (2000), no.3, 459-475.

TAYLOR B.D.,
[1] Difference equations via the classical umbral calculus. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 397-411, Progr. Math., 161, Birkhäuser Boston, Boston, MA, 1998.

TUENTER H.J.H.,
[1] A Symmetry of Powersum Polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261.

ZHANG WEI RONG,
[1] Using a Newtonian formula to prove a theorem of Euler. (Chinese.) J. Nanjing Norm. Univ. Nat. Sci. Ed. 22 (1999), no. 1, 16-17.

March 9, 2001:

KANEKO M.,
[4] The Akiyama-Tanigawa algorithm for Bernoulli numbers. J. Integer Seq. 3 (2000), no. 2, Article 00.2.9, 6 pp. (electronic).

FOX, G.J.,
[3] Congruences relating rational values of Bernoulli and Euler polynomials. Fibonacci Quart. 39 (2001), no. 1, 50-57.

February 10, 2001:

JANG YOUNGHO, KIM MIN-SOO, SON JIN-WOO,
[1] An analogue of Bernoulli numbers and their congruences. Proc. Jangjeon Math. Soc. 1 (2000), 133-143.

KIM TAEKYUN, RIM SEOG-HOON,
[3] Explicit formulas for the $q$-Bernoulli numbers of higher order. Proc. Jangjeon Math. Soc. 1 (2000), 97-107.

KOZUKA K.,
[6] On linear combinations of $p$-adic interpolating functions for the Euler numbers. Kyushu J. Math. 54 (2000), no. 2, 403-421.

BRESSOUD D.M.,
[1] A radical approach to real analysis. Mathematical Association of America, Washington, DC, 1994. xii+324 pp.

THOMPSON W.J.,
[1] Atlas for computing mathematical functions. An illustrated guide for practioners with programs in C and Mathematica. Incl. 1 CD-ROM. Chichester: Wiley. xiv, 903 p. (1997).

[2] Atlas for computing mathematical functions: an illustrated guide for practitioners, with program in Fortran 90 and Mathematica. Incl. 1 CD-ROM. Chichester: John Wiley & Sons. xiv, 888 p. (1997).

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