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J. Korean Math. Soc. 2003; 40(6): 963-975
Printed November 1, 2003
Copyright © The Korean Mathematical Society.
On $q$-analgue of the twisted $L$-functions and $q$-twisted Bernoulli numbers
Yilmaz Simsek
University of Mersin Faculty of Science
The aim of this work is to construct twisted $q$-$L$-series which interpolate twisted $q$-generalized Bernoulli numbers. By using generating function of $q$-Bernoulli numbers, twisted $q$-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\chi,\xi)$ is also given explicitly.
Keywords: Dirichlet $L$-functions, twisted $L$-functions, Hurwitz zeta function, generalized Bernoulli numbers and polynomials, $q$-analogues of the Dirichlet series and $q$-$L$-series, $q$-Bernoulli numbers
MSC numbers: Primary 11M41; Secondary 11B68, 11M35
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