[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2002.39.2.221

SOME REMARKS ON A q-ANALOGUE OF BERNOULLI NUMBERS

Kim, Min-Soo (Department of Mathematics, Kyungnam University)
Son, Jin-Woo (Department of Mathematics, Kyungnam University)

Publication Information

Journal of the Korean Mathematical Society / v.39, no.2, 2002 , pp. 221-236 More about this Journal

Abstract

Using the p-adic q-integral due to T. Kim[4], we define a number B＊ $_{n}$ (q) and a polynomial B＊ $_{n}$ (q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura＇s p-adic function $\ell$ $_{p}$ (u, s, $\chi$ ) [14] using the p-adic q-integral in [4].n [4].

Keywords

q-analogue; Bernoulli numbers. p-adic q-integral;

Citations & Related Records

Times Cited By KSCI : 3 (Citation Analysis)
Times Cited By Web Of Science : 2 (Related Records In Web of Science)
Times Cited By SCOPUS : 2

1	Remark on p-adic q-Bernoulli numbers / [ T. Kim;H. S. Kim ] / Advanced Studies in Contemporary Math.
2	q-Bernoulli numbers and polynomials / [ L. Carlitz ] / Duke Math. J. DOI
3	On a q-analogue of the p-adic log gamma functions and related integral / [] / J. Number Theory DOI ScienceOn
4	A note on the values of zeta / [] / Notes Number Theory Discrete Math.
5	On a p-adic interpolation of the generalized Euler numbers and its applications / [ H. Tsumura ] / Tokyo J. Math. DOI
6	On explicit formulas of p-adic q-L-functions / [] / Kyushu J. Math. DOI
7	A new proof of certain formulas for p-adic L-functions / [ N. Koblitz ] / Duke Math. J. DOI
8	/ [ L. Washington ] / Introduction to Cyclotomic Fields, 2nd
9	A note on q-analogues of the Dirichlet series and q-Bernoulli numbers / [] / J. Number Theory DOI
10	q-analogue of Riemann’s ³-function and q-Euler numbers / [ J. Satoh ] / J. Number Theory DOI
11	On Bernoulli numbers / [ M.-S. Kim;J.-W. Son ] / J. Korean Math. Soc. 과학기술학회마을
12	A remark on p-adic q-Bernoulli measure / [ H. S. Kim;P.-S. Lim;T. Kim ] / Bull. Korean Math. Soc. 과학기술학회마을
13	/ [] / p-adic Numbers, p-adic Analysis and Zeta-Functions, 2nd
14	An analogue of Bernoulli numbers and their congruences / [ T. Kim ] / Rep. Fac. Sci. Engrg. Saga Univ. Math.
15	On Carlitz’s q-Bernoulli numbers / [] / J. Number Theory DOI
16	A note on p-adic Dedekind sums / [] / Comptes Rendus De l’Academine Bulgare des Sciences

Yilmaz Simsek. (2005) Journal of Number Theory
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1	ON TWISTED GENERALIZED EULER NUMBERS / [Simsek, Yilmaz;] / Bulletin of the Korean Mathematical Society
2	ANALYTIC PROPERTIES OF THE q-VOLKENBORN INTEGRAL ON THE RING OF p-ADIC INTEGERS / [Kim, Min-Soo;Son, Jin-Woo;] / Bulletin of the Korean Mathematical Society

1	/ Journal of Number Theory
2	/ Bulletin of the Korean Mathematical Society