Bernoulli Bibliography

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JACOBI C.G.J.,
[1] De usu legitimo formulae summatoriae Maclaurinianae, J. Reine Angew. Math., 12 (1834), 263-272.

JACOBSON M.J., Jr., PINTÈR, Á., WALSH P.G.,
[1] A computational approach for solving $y\sp 2=1\sp k+2\sp k+\dots+x\sp k$. Math. Comp. 72 (2003), no. 244, 2099-2110.
M2004c:11241

JACOBSTHAL E.,
[1] Über eine Formel von Frobenius, Kgl. Norske Videns. Selsk. Forh. Trondheim, 22 (1950), 51-55.
Z36.01201; M11-653e

[2] Zur Theorie der Bernoullischen Zahlen, Norske Vid. Selsk. Forh. Trondheim, 22 (1950), no. 24, 107-112.
Z36.01202; M11-581b

[3] Number-theoretical propeties of binomial coefficients (Norwegian), Norske Vid. Selsk. Skr., Trondhjem, 1942, no. 4, 28pp. (1945).
M8-314d

JACOBSTHAL E.: see also BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.

JAKUBEC S.,
[1] On Vandiver's conjecture, Abh. Math. Sem. Univ. Hamburg, 64 (1994), 105-124.
Z828.11050; M95h:11116

[2] On divisibility of the class number of real octic fields of a prime conductor $p=n^4+16$ by $p$. Arch. Math. (Brno), 30 (1994), no. 4, 263-270.
Z818.11042; M96a:11120; R1999,1A244

[3] On the divisibility of $h\sp +$ by the prime $3$. Rocky Mountain J. Math. 24 (1994), no. 4, 1467-1473.
Z821.11053; M95m:11119

[4] Congruence of Ankeny-Artin-Chowla type for cyclic fields of prime degree $l$. Math. Proc. Cambridge Philos. Soc., 119 (1996), no. 1, 17-22.
Z853.11085; M96j:11145

[5] Congruence of Ankeny-Artin-Chowla type modulo $p\sp 2$ for cyclic fields of prime degree $l$. Acta Arith. 74 (1996), no. 4, 293-310.
Z853.11086; M97h:11135

[6] Connection between congruences $n\sp {q-1}\equiv 1\pmod {q\sp 2}$ and divisibility of $h\sp +$, Abh. Math. Sem. Univ. Hamburg, 66 (1996), 151-158.
Z871.11075; M98a:11145

[7] On divisibility of the class number $h\sp +$ of the real cyclotomic fields of prime degree $l$. Math. Comp. 67 (1998), no. 221, 369-398.
Z914.11057; M98d:11136; R1999,3A230

[8] Note on Wieferich's congruence for primes $p \equiv 1 \pmod{4}$, Abh. Math. Sem. Univ. Hamburg, 68 (1998), 193-197.
M99i:11012

[9] Note on the congruence of Ankeny-Artin-Chowla type modulo $p\sp 2$, Acta Arith. 85 (1998), no. 4, 377-388.
Z912.11041; M99m:11128; R1999,8A309

[10] Congruence of Ankeny-Artin-Chowla type for cyclic fields. Math. Slovaca 48 (1998), no. 3, 323-326.
Z939.11036; M99j:11127; R00.06-13A216

[11] Connection between Schinzel's conjecture and divisibility of the class number $h\sp +\sb p$. Acta Arith. 94 (2000), no. 2, 161-171.
Z954.11034; M2001c:11122; R01.06-13A256

[12] Remark on certain sums concerning class number. Abh. Math. Sem. Univ. Hamburg, 71 (2001), 69-76.
Z0998.11057; M2002i:11108

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.
Z923.11154; M99m:11127; R00.06,13A217

JAMES R. D.,
[1] On the expansion coefficients of the functions $u/sn\;u$ and $u^2/sn^2u$. Bull. Amer. Math. Soc., 40 (1934), 632-640.
J60.1056.01; Z9.40001

JAMIESON A.M.,
[1] An expression for Bernoulli numbers, Proc. Glasgow Math. Assoc., 1 (1953), 126-128.
Z53.23103; M15-289g

JANG DOUK SOO: see SON JIN-WOO, JANG DOUK SOO

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.
M2003m:11034

[2] A note on the twisted $q$-zeta functions and the twisted $q$-Bernoulli polynomials. Proceedings of the 15th International Conference of the Jangjeon Mathematical Society, 57--62, Jangjeon Math. Soc., Hapcheon, 2004.
M2005m:11030

JANG L.C., KIM J.H., KIM T., LEE D.H., PARK D.W., RYOO C.S.,
[1] On Witt's formula for the Barnes' multiple Bernoulli polynomials. Far East J. Math. Sci. (FJMS) 13 (2004), no. 3, 309-317.

JANG LEE-CHAE, KIM TAEKYUN, LEE DEOK-HO, PARK DAL-WON,
[1] An application of polylogarithms in the analogs of Genocchi numbers. Notes Number Theory Discrete Math. 7 (2001), no. 3, 65-69.

JANG LEECHAE, KIM TAEKYUN, PARK DAL-WON,
[1] Kummer congruence for the Bernoulli numbers of higher order. Appl. Math. Comput. 151 (2004), no. 2, 589-593.
M2004k:11018

Jang, Lee-Chae; Kim, Seoung-Dong; Park, Dal-Won; Ro, Young-Soon,
[1] A note on Euler number and polynomials. J. Inequal. Appl. 2006, Art. ID 34602, 5 pp.
M2007c:11022

JANG LEECHAE, KIM TAEKYUN, RIM SEOG-HOON,
[1] A note on the generalized $q$-Bernoulli numbers. Far East J. Math. Sci. (FJMS) 13 (2004), no. 1, 29-37.

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.
M2001j:11114

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.
M2003m:11201

JANG LEE CHAE, PAK HONG KYUNG, RIM SEOG-HOON, PARK DAL-WON,
[1] A note on analogue of Euler and Bernoulli numbers. JP J. Algebra Number Theory Appl. 3 (2003), no. 3, 461-469.
M2005b:11021

JANG L.C.: see also KIM T., JANG L.C., RYOO C.S., PARK D.-W.

JANG LEE-CHAE: see also KIM TAEKYUN, JANG LEE-CHAE, PAK HONG KYUNG.

JANG LEE-CHAE: see also KIM TAEKYUN, JANG LEE CHAE, RIM SEOG-HOON, PAK HONG-KYUNG.

JANG LEE-CHAE: see also KIM YUNG-HWAN, PARK DAL-WON, JANG LEE-CHAE.

JANG YOUNGHO, KIM DAE SAN,
[1] On higher order generalized Bernoulli numbers. Appl. Math. Comput. 137 (2003), no. 2-3, 387-398.
M2003m:11035

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.
Z0990.11009; M2002i:11022

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.
M2001i:11142

JANIC R.R., MITROVIC Z.M.,
[1] Bernoulli and Euler polynomials in k variables, Univ. Beograd. Publ. Elektrotechn. Fak. Ser. Math. Fiz., No. 412-460 (1973), 75-78.
Z274.33012; M48#6478; R1974,4V257

JANKOVIC Z.,
[1] Summen der gleichen Potenzen der natürlichen Zahlen, Zeitschrift für math. u. naturwiss. Unterricht 74 (1943), 41-44.
Z063.03036

[2] Jeden izvod Bernoullieve formule [Une démonstration de la formule de Bernoulli]. (Serbo-Croatian. French summary.), Glasnik Mat.-Fiz. Astr. Ser. II, 7 (1952), 23-29.
Z82.01702; M13-913a

[3] Two recurrence formulae for the sums $s_{2k}$. Hrvatsko Prirodoslovno Drustvo. Glasnik Mat.-Fiz. Astr. Ser. II., 8 (1953), 27-29.
Z53.03901; M14-974b

JAULENT J.-F.: see GRAS G., JAULENT J.-F.

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.

M2001k:11212

JEFFERY H.M.,
[1] On Staudt's proposition relating to the Bernouillian numbers, Quart. J. Math., 6 (1864), 179-180.

JENSEN K.L.,
[1] Om talteoretiske Egenskaber ved de Bernoulliske Tal, Nyt Tidskr. f. Math., 26 (1915), 73-83.
J45.1257.08

[2] Note sur la congruence de Kummer relative aux nombres de Bernoulli, Overs. Danske Vidensk. Selsk. Forh., (1915), 321-331.
J45.0304.01; J45.0304.02

Jeong, Sangtae; Kim, Min-Soo; Son, Jin-Woo,
[1] On explicit formulae for Bernoulli numbers and their counterparts in positive characteristic. J. Number Theory 113 (2005), no. 1, 53-68.
M2006h:11019

JETTER K.,
[1] The Bernoulli spline and approximation by trigonometric blending polynomials, Resultate Math., 16 (1989), no. 3-4, 243-252.
Z682.42001; M91a:41009; R1990,4B109

JHA V.,
[1] Faster computation of irregular pairs corresponding to an odd prime. J. Indian Math. Soc., 59 (1993), no. 1-4, 149-152.
Z865.11088; M95d:11173

[2] The Stickelberger Ideal in the Spirit of Kummer with Appllication to the First Case of Fermat's Last Theorem. Queen's Papers in Pure and Applied Mathematics, No. 93. Kingston, Ontario 1993. xiv + 181 pp.
Z779.11057; M95d:11148

[3] On Krasner's theorem for the first case of Fermat's last theorem, Colloq. Math., 67 (1994), no. 1, 25-31.
Z813.11009; M95h:11025

JI CHUN-GANG: see BUNDSCHUH P., JI CHUN-GANG, SHAN ZUN

JIANG ZENG: see RANDRIANARIVONY A., JIANG ZENG

JIN JIANMING: see ZHANG SHANJIE, JIN JIANMING

JIN JINGYU: see ZHANG ZHIZHENG, JIN JINGYU

JOCHNOWITZ N.,
[1] A $p$-adic conjecture about derivatives of $L$-series attached to modular forms. $p$-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), 239--263, Contemp. Math., 165, Amer. Math. Soc., Providence, RI, 1994.
Z869.11040; M95g:11037

JOFFE S.A.,
[1] Sums of like powers of natural numbers. Quart. J. Math., 46 (1915), 33-51.
J45.1244.02

[2] Calculation of the first thirty-two Eulerian numbers from the central differences of zero. Quart. J. Pure Appl. Math., 47 (1916), 103-126.
J46.0360.03

[3] Calculation of Eulerian numbers from central differences of zero. (Abstract) Bull. Amer. Math. Soc., 22 (1916), 381.
J46.0360.02

[4] Calculation of eighteen more, fifty in all, Eulerian numbers from central differences of zero, Quart. J. Pure Appl. Math., 48 (1919), 193-271.

JOHNSEN J.,
[1] On the distribution of irregular primes, J. Number Theory, 8 (1976), no. 4, 434-437.
Z339.10012; M55#5552; R1977,5A60

JOHNSON W.,
[1] On the vanishing of the Iwasawa invariant $\mu_p$ for $p < 8000$, Math. Comp., 27 (1973), 387-396.
Z281.12006; M52#5621; R1974,1A355

[2] Irregular prime divisors of the Bernoulli numbers, Math. Comp., 28 (1974), no. 126, 653-657.
Z293.10008; M50#229; R1974,12A129

[3] Irregular primes and cyclotomic invariants, Math. Comp., 29 (1975), no. 129, 113-120.
Z302.10020; M51#12781; R1975,12A160

[4] On the distribution of quadratic residues (Abstract), Notices Amer. Math. Soc., 22 (1975), no. 1, A66.

[5] p-adic proofs of congruences for the Bernoulli numbers, J. Number Theory, 7 (1975), no. 2, 251-265.
Z308.10006; M51#12687; R1975,12A117

JOHNSONBAUGH R.,
[1] Summing an alternating series, Amer. Math. Monthly, 86 (1979), no. 8, 637-648.
Z425.65002; M80g:40003; R1980,8B19

JOLY J.-R.,
[1] Calcul des nombres de Bernoulli modulo $p^m$. Application à l'étude des nombers premiers irreguliers. Sémin. Théor. Nombres, Univ. Grenoble I, (1980-1981). Exposé No.4, (1981), 19pp.
Z475.10013

[2] Analyse numérique p-adique des nombres de Bernoulli et des séries $L$ de Dirichlet. Sémin. Théor. Nombres, Univ. Grenoble I, (1981-82). Exposé No.6, (1982), 14pp.
Z506.10010

[3] Calcul des nombres de Bernoulli modulo $p^m$, Sémin. Théor. Nombres, Paris, (1981-82), 113-124. Sémin. Delange-Pisot-Poitou, Progr. Math., 38, Birkhäuser, Boston, Mass., 1983.
Z536.10011; M85g:10023; R1984,8A101

JONES G.A., JONES J.M.,
[1] Elementary number theory. Springer-Verlag London, Ltd., London, 1998. xiv+301 pp.
Z891.11001; M2000b:11002

JONQUIERE A.,
[1] Note sur la série $\sum_{n=1}^{n=\infty}{{x^n}\over{n^s}}$. Bull. Soc. Math. France, 17 (1889), no.5, 142-152.
J21.0246.02

[2] Note sur la série $\sum_{n=1}^{n=\infty}{{x^n}\over{n^s}}$. Översigt Kongl. Vet.-Akad. Förhandl., 5 (1889), 257-268.
J21.0247.01

[3] Über eine Verallgemeinerung der Bernoulli'schen Funktionen und ihren Zusammenhang mit der verallgemeinerten Riemann'schen Reihe. Bihang K. Svenska Vet.-Akad. Handl., 16 (1891), no. 6, 1-28.
J23.0432.01

JORDAN CH.,
[1] Calculus of finite differences, 2nd ed., Chelsea Publ. Co., New York, 1950, xxi +652 pp.
Z41.05401; M1-74e

[2] Sur des polynomes analogues aux polynomes de Bernoulli et sur des formules de sommation analogues à celle de Maclaurin-Euler. Acta Scientiarum Math.(Szeged), 4 (1929), 130-150.
J55.0266.02

JOSHI J.M.C.: see SRIVASTAVA H.M., JOSHI J.M.C., BISHT C.S.

JUNG W.,
[1] Poznamka k cislum Bernoulliho [A note on Bernoulli numbers], Casopis Pest. Mat. Fyz., 9 (1880), 103-108.
J12.0195.01


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