Bernoulli Bibliography

Publications added in 2004


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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.
December 31, 2004:

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.

KIM T., JANG L.C., RYOO C.S., PARK D.-W.,
[1] The real zeros of $q$-Bernoulli polynomials. Far East J. Appl. Math. 16 (2004), no. 2, 233-248.

KIM T.
[2] $p$-adic $q$-integrals associated with the Changhee-Barnes' $q$-Bernoulli polynomials. Integral Transforms Spec. Funct. 15 (2004), no. 5, 415-420.

BRETTI G., NATALINI P., RICCI P.E.,
[1] Generalizations of the Bernoulli and Appell polynomials. Abstr. Appl. Anal. 2004, no. 7, 613-623.

MINH HOANG N.,
[1] Finite polyzetas, poly-Bernoulli numbers, identities of polyzetas and noncommutative rational power series. Proceedings of WORDS'03, 232--250, TUCS Gen. Publ., 27, Turku Cent. Comput. Sci., Turku, 2003.

LIU GUO DONG,
[11] Solution of a problem for Euler numbers. (Chinese) Acta Math. Sinica 47 (2004), no. 4, 825-828.

CENKCI M., CAN MIMIN, KURT V.,
[1] $p$-adic interpolation functions and Kummer-type congruences for $q$-twisted and $q$-generalized twisted Euler numbers. Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), no. 2, 203-216.

KIM TAEKYUN, RIM SEOG-HOON,
[5] On Changhee-Barnes' $q$-Euler numbers and polynomials. Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), no. 2, 81-86.

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.

October 20, 2004:

EIE M., ONG Y.L.,
[3] On sums of certain trigonometric series. Bull. Austral. Math. Soc. 67 (2003), no. 1, 103-114.

GREENE J.,
[1] The Burgstahler coincidence. Fibonacci Quart. 40 (2002), no. 3, 194-202.

JACOBSON M.J., Jr., PINTÉR, 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.

KIM TAEKYUN,
[7] Remark on $p$-adic proofs for $q$-Bernoulli and Eulerian numbers of higher order. Proc. Jangjeon Math. Soc. 2 (2001), 9-15.

[8] Some $q$-Bernoulli numbers of higher order associated with the $p$-adic $q$-integers. Proc. Jangjeon Math. Soc. 2 (2001), 23-28.

[9] A note on $p$-adic $q$-Dedekind sums. Proc. Jangjeon Math. Soc. 2 (2001), 29-34.

[10] A note on $p$-adic $q$-Dedekind sums. C. R. Acad. Bulgare Sci. 54 (2001), no. 10, 37-42.

[11] A note on the solutions for exercise problems of $p$-adic $q$-integrals. Proc. Jangjeon Math. Soc. 2 (2001), 45-49.

KOZUKA K.,
[7] Dedekind type sums attached to Dirichlet characters. Kyushu J. Math. 58 (2004), no. 1, 1-24.

LIU GUO DONG,
[10] Generalizations of Vassilev's formula. (Chinese. English summary) Gongcheng Shuxue Xuebao 19 (2002), no. 4, 95-100.

LIU TONG,
[1] The Ankeny-Artin-Chowla formula over sextic cyclic number fields. (Chinese) Kexue Tongbao (Chinese) 43 (1998), no. 5, 471-474.

[2] Formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic sextic fields. Chinese Sci. Bull. 43 (1998), no. 10, 824-826.

PRODINGER H.,
[3] On Cantor's singular moments. Southwest J. Pure Appl. Math. 2000, no. 1, 27-29 (electronic).

RAMAKRISHNAN B., THANGADURAI R..,
[1] A note on certain divisibility properties of the Fourier coefficients of normalized Eisenstein series. Expo. Math. 21 (2003), no. 1, 75-82.

SHIMADA T.,
[2] An application of the Fermat quotient of units to the method of Kim. Abh. Math. Sem. Univ. Hamburg 71 (2001), 1-14.

SLAVUTSKII I.SH.,
[37] Real quadratic field and Ankeny-Artin-Chowla conjecture. J. Math. Sci. (N.Y.) 122 (2004), no.6., 3673-3678. (Translation of [36]).

VOROS A.,
[3] Zeta functions for the Riemann zeros. Ann. Inst. Fourier (Grenoble) 53 (2003), no. 3, 665-699.

YOSHIDA H.,
[2] Absolute CM-periods. Mathematical Surveys and Monographs, 106. American Mathematical Society, Providence, RI, 2003. x+282 pp. ISBN 0-8218-3453-3.

ZHANG JING, FANG JIAN PING,
[1] A generalization of Wolstenholme's theorem. (Chinese. English, Chinese summa ry) J. Nanjing Norm. Univ. Nat. Sci. Ed. 23 (2000), no. 1, 19-20.

October 18, 2004:

ADELBERG A.,
[11] Universal Bernoulli polynomials and $p$-adic congruences. Applications of Fibonacci numbers. Vol. 9, 1-8, Kluwer Acad. Publ., Dordrecht, 2004.

AKIYAMA S., TANIGAWA Y.,
[1] Multiple zeta values at non-positive integers. Ramanujan J. 5 (2001), no. 4, 327-351 (2002).

CHEN KWANG-WU,
[3] Congruences for Euler numbers. Fibonacci Quart. 42 (2004), no. 2, 128-140.

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.

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, 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.

KIM T.
[1] Non-Archimedean $q$-integrals associated with multiple Changhee $q$-Bernoulli polynomials. Russ. J. Math. Phys. 10 (2003), no. 1, 91-98.

KIM TAEKYUN,
[14] Remark on the multiple Bernoulli numbers. Proc. Jangjeon Math. Soc. 6 (2003), no. 2, 185-192.

KIM TAEKYUN, ADIGA C.,
[1] Sums of products of generalized Bernoulli numbers. Int. Math. J. 5 (2004), no. 1, 1-7.

KIM TAEKYUN, JANG LEE CHAE, RIM SEOG-HOON, PAK HONG-KYUNG,
[1] On the twisted $q$-zeta functions and $q$-Bernoulli polynomials. Far East J. Appl. Math. 13 (2003), no. 1, 13-21.

LEE WILL Y.
[1] On fractional Bernoulli numbers. Kyungpook Math. J. 44 (2004), no. 1, 69-75.

LIU HUANING, ZHANG WENPENG,
[1] On the hybrid mean value of Gauss sums and generalized Bernoulli numbers. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 6, 113-115.

LUO QIU MING,
[3] Euler polynomials of higher order involving the stirling numbers of the second kind. Austral. Math. Soc. Gaz. 31 (2004), no. 3, 194-196.

LUO QIU MING, AN CHUN XIANG,
[1] Relations between Bernoulli numbers of higher order and Euler numbers of higher order. (Chinese) J. Henan Norm. Univ. Nat. Sci. 32 (2004), no. 2, 28-30, 37.

LUO QIU-MING, GUO BAI-NI, QI FENG, DEBNATH L.,
[1] Generalizations of Bernoulli numbers and polynomials. Int. J. Math. Math. Sci. 2003, no. 59, 3769-3776.

LUO QIU-MING, QI FENG, DEBNATH L.,
[1] Generalizations of Euler numbers and polynomials. Int. J. Math. Math. Sci. 2003, no. 61, 3893-3901.

MATIYASEVICH Yu.V.,
[2] A Diophantine representation of Bernoulli numbers and its applications. (Russian) Dedicated to the 100th birthday of Academician Petr Sergeevich Novikov (Russian). Tr. Mat. Inst. Steklova 242 (2003), Mat. Logika i Algebra, 98-102.

RYOO CHEON SEOUNG, KIM TAEKYUN,
[1] Beautiful zeros of $q$-Euler polynomials of order $k$. Proc. Jangjeon Math. Soc. 7 (2004), no. 1, 63-79.

RZADKOWSKI G.,
[1] A short proof of the explicit formula for Bernoulli numbers. Amer. Math. Monthly 111 (2004), no. 5, 432-434.

SHANNON A.G.,
[3] Generalized Bernoulli polynomials & Jackson's calculus of sequences. Notes Number Theory Discrete Math. 9 (2003), no. 1, 1-6.

SIMSEK Y.,
[1] On $q$-analogue of the twisted $L$-functions and $q$-twisted Bernoulli numbers. J. Korean Math. Soc. 40 (2003), no. 6, 963-975.

[2] On twisted generalized Euler numbers. Bull. Korean Math. Soc. 41 (2004), no. 2, 299-306.

SINGH A.P., L. R.M.,
[1] A $k$-variable extension of Bernoulli and Euler polynomials of general order. Acta Cienc. Indica Math. 29 (2003), no. 2, 353-357.

SRIVASTAVA H.M., PINTÉR Á.,
[1] Remarks on some relationships between the Bernoulli and Euler polynomials. Appl. Math. Lett. 17 (2004), no. 4, 375-380.

THANGADURAI R.,
[1] Adams theorem on Bernoulli numbers revisited. J. Number Theory 106 (2004), no. 1, 169-177.

TSUMURA H.,
[6] Multiple harmonic series related to multiple Euler numbers. J. Number Theory 106 (2004), no. 1, 155-168.

YOUNG P.T.,
[4] Degenerate and $n$-adic versions of Kummer's congruences for values of Bernoulli polynomials. Discrete Math. 285 (2004), no. 1-3, 289-296.

ZHENG YU MIN, LUO QIU MING,
[1] The recursion formulas of higher-order Bernoulli numbers. (Chinese) Math. Practice Theory 33 (2003), no. 8, 116-119.


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