A q-Analogue of the Dirichlet L-Function

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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 Boulli 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 Boulli numbers and the generalized Euler numbers. As an application, we prove that the q-analogue of Boulli numbers occurs in the coefficients of some Stirling type series for the p-adic analytic q-log-gamma function.
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