On the values of p-adic q-L-functions. II

Lee Chae Jang, Taekyun Kim and Hong Kyung Раk
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 8, 2002, Number 1, Pages 21–27
Full paper (PDF, 2427 Kb)

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Authors and affiliations

Lee Chae Jang
Department of Math, and Comput. Sciences Konkuk University, Chungju, S. Korea

Taekyun Kim
Institute of Science Education Kongju National University, Kongju, S. Korea

Hong Kyung Раk
Department of Mathematics Kyungsan University, Kyungsan, S. Korea

Abstract

In the recent paper, we defined the h-extension of q-Bernoulli number by using multiple p-adic q-integral and constructed the h-extension of complex analytic q-L-series which interpolates the h-extension of q-Bernoulli numbers, cf. [2], [4], [5]. The purpose of this paper is to construct a h-extension of p-adic q-L-function which interpolates the h-extension of q-Bernoulli numbers at non-positive integers.

Keywords

• Bernoulli numbers
• p-adic
• q-L-function
• p-adic q-integrals

2010 Mathematics Subject Classification

• 11B68
• 11S80

References

1. T. Kim et al, A note on the analogs of p-adic L-functions and sums of powers, Notes on Number Theory and Discrete Math. 7 No. 3 (2001).
2. T. Kim and S.H. Rim, Generalized Carlitz’s q-Bernoulli numbers in the p-adic number field, Advanced Stud. Contemp. Math. 2 (2000), 9-19.
3. T. Kim, On explicit formulas of p-adic q-L-functions, Kyushu J. Math. 48 (1994), 73-86.
4. T. Kim, H.S. Kim, On the values of p-adic q-L-functions, Pusan Kyoungnam Math. J. 11 (1995), 55-64.
5. T.Kim, A note on p-adic q-Dedekind Sums, Comptes Rend. L’Acad. Bulga. Sci. 54 (2001), 37-42.
6. T. Kim, On certain values of p-adic q-L-functions, Rep. Fac. Sci. Engrg. Saga Univ. Math. 23 (1996), 1-7.
7. N. Kobiltz, On Carlitz’s q-Bernoulli numbers, J. Number Theory 14 (1982), 332-339.
8. J. Satoh, q-analogue of Riemann’s (ζ-function and q-Euler numbers, J. Number Theory 31 (1989), 346-362.
9. L. C. Washington, p-adic L-functions and sums of powers, J. Number Theory 69 (1998), 50-61.