Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2007; 44(1): 1-10

Printed January 1, 2007

Copyright © The Korean Mathematical Society.

On a $q$-analogue of the $p$-adic generalized twisted $L$-functions and $p$-adic $q$-integrals

Lee-Chae Jang

KonKuk University

Abstract

The purpose of this paper is to define generalized twisted $q$-Bernoulli numbers by using $p$-adic $q$-integrals. Furthermore, we construct a $q$-analogue of the $p$-adic generalized twisted $L$-functions which interpolate generalized twisted $q$-Bernoulli numbers. This is the generalization of Kim's $h$-extension of $p$-adic $q-L$-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

Keywords: $p$-adic integrals, $p$-adic twisted $L$-functions, $q$-Bernoulli numbers

MSC numbers: 11B68, 11S80