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

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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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

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  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.

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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 Zp. Notes on Number Theory and Discrete Mathematics, 7(4), 105-110.

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