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

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## 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

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

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## Cite this paper

Pak, H. K. & Rim, S.-H. (2001). *q*-Bernoulli numbers and polynomials via an invariant *p*-adic *q*-integral in Z* _{p}*. Notes on Number Theory and Discrete Mathematics, 7(4), 105-110.