q-Bernoulli numbers and polynomials via an invariant p-adic q-integral in Z_p

H. K. Pak and S.-H. Rim
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 7, 2001, Number 4, Pages 105–110
Full paper (PDF, 87 Kb)

Details

Authors and affiliations

H. K. Pak
Department of Mathematics Kyungsan university,
Kyungsan, S. Korea

S.-H. Rim
Department of mathematics Education Kyungpook Unversity,
Taegu 702-701, S. Korea

Abstract

We define the q-Bernoulli numbers by using an p-adic q-integral due to T. Kim and investigate the properties of these numbers. In the final section, we will give the formula for sums of products of these numbers.

AMS Classification

• 11B68
• 11S40

References

1. L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math J. 15 (1948), 987-1000.
2. K. Dilcher, Sums of products of Bernoulli numbers, J. Number Theory 60(1) (1996), 23-41.
3. I. C. Huang, Bernoulli numbers and polynomials via residue, J. Number Theory 76 (1999), 178193.
4. T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory 76 (1999), 320-329.
5. T. Kim and H.S. Kim, Remark on p-adic q-Bernoulli numbers, Advan. Stud. Contemp. Math. 1 (1999), 127-136.
6. K. Kudo, A congruence of generalized Bernoulli numbers for the character of the first kind, Advan. Stud. Contemp. Math. 2 (2000), 1-8.
7. J. Satoh, Sums of products of two q-Bernoulli numbers, J. Number Theory 74 (1999), 173-180.