q-Hardy-Berndt type sums associated with q-Genocchi type zeta and l-functions

Abstract

The aim of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function, q-analogue Genocchi type l-function and two-variable q-Genocchi type l-function. Furthermore, we construct new genereting functions of q-Hardy-Berndt type sums and q-Hardy-Berndt type sums attached to Dirichlet character. We also give some new relations related to q-Hardy-Berndt type sums and q-Genocchi zeta function as well.

22 pages

References in corpus (3)

• $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
• q-Multiple Zeta Functions and q-Multiple Polylogarithms
• On the two-variable Dirichlet q-L-series

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