A q-Analogue of the Dirichlet L-Function

• 来源期刊: 代数集刊（英文版）
• 关键词: q-analogue ζ-function L-series p-adic log gamma function
• 年，卷（期）: 2002,（4）
• 页码范围: 469-480
• 页数: 12页
• 语种: 英文

摘要

In this paper, we will treat some interesting formulae which are slightly different from Kim's results by more or less the same method in [4-9]. At first, we consider a new definition of a q-analogue of Bernoulli numbers and polynomials.We construct a q-analogue of the Riemann ζ-function, Hurwitz ζ-function, and Dirichlet L-series. Also, we investigate the relation between the q-analogue of generalized Bernoulli numbers and the generalized Euler numbers. As an application, we prove that the q-analogue of Bernoulli numbers occurs in the coefficients of some Stirling type series for the p-adic analytic q-log-gamma function.