An invariant integrals in the p-adic number fields

Lee Chae Jang
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 8, 2002, Number 3, Pages 107–111
Full paper (PDF, 174 Kb)

Details

Authors and affiliations

Lee Chae Jang
Department of Mathematics and Computer Science
KonKuk University, Chungju 380-701, S. Korea

Abstract

In this paper we investigate some properties of non-Archimedean integration which is defined by T. Kim, cf. [2]. By using our results in this paper, we can give an answer of the problems which is remained by I.-C. Huang and S-Y. Huang in [1: p. 179]

References

1. I.-C. Huang, S.-Y. Huang, Bernoulli numbers and polynomials via residues, J. Number Theory 76 (1999), 178-193.
2. T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory 76 (1999), 320-329.
3. T. Kim, L.C. Jang and H. K. Pak, A note on q-Euler numbers and Genocchi numbers, Proc. Japan Acad. Ser A Math. Sci. 77 (2001), 139-141.
4. K. Shiratani and S. Yamamoto, On a p-adic interpolation function for the Euler numbers and its derivatives, Mem. Fac. Sci. Kyushu Univ., 39 (1985), 113-125.
5. H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc., 129 (2000), 77-84.
6. H.M. Srivastava and P.G. Todorov, An explicit formula for the generalized Bernoulli polynomials, J. Math. Anal.Appl., 130 (1988), 509-513.
7. H.M. Srivastava, Series Associated with the Zeta and Related Functions, Kluwer Acad Publishers (Dor- dreht/Boston/London), 2001.