T. Kim, C.S. Ryoo, H. K. Pak and S.-H. Rim

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 7, 2001, Number 3, Pages 78—86

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## Details

### Authors and affiliations

T. Kim,

*Institute of Science Education,
Kongju National University, Kongju 314-701, S. Korea
*

C.S. Ryoo

*Deaprtment of Mathematics ,
Kyungpook University, Taegu 702-701, S. Korea*

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

The purpose of this paper is to give an explicit *p*-adic expansion of such that the coefficients of the expansion are the values of an analogue of *p*-adic *L*-function associated with Euler numbers.

### Keywords

*p*-adic*L*-function- Bernoulli numbers
- Dirichlet’s series

### AMS Classification

- 11B68
- 11S80

### References

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*p*-adic*q*-Dedekind sums, Comptes Rendus de l’Academie Bulgare des Sciences 54 no. 10 (2001), 37-42. - ______, Remark on
*p*-adic*q*-Bernoulli numbers, Adv. Stud. Contemp. Math. (Kudeok Publ.) 1 (1999), 127-136. - ______, Some
*q*-Bemoulli numbers of higher order associated with the*p*-adic q-integrals, Indian J. Pure and Appl. Math. 32 no. 10 (2001), 1565-1570. - ______, An analogue of Bernoulli numbers and their congruences, Rep. Fac. Sci. Engrg. Saga Univ. Math. 22 (1994), 7-13.
- L.C. Jang, T. Kim, D-H. Lee, D-W. Park, An application of polylogarithms in the analogs of Genocchi numbers, Notes on Number Theory and Discrete Mathematics 7 no. 3 (2001), 65-69.
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## Cite this paper

Kim, T. , Ryoo, C.S., Pak, H. K. & Rim, S.-H. (2001). A note on the analogs of *p*-adic *L*-functions and sums of powers. Notes on Number Theory and Discrete Mathematics, 7(3), 78-86.