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

Abstract

The aim of this paper is to define new generating functions. By applying a derivative operator and the Mellin transformation to these generating functions, we define q -analogue of the Genocchi zeta function, q -analogue Hurwitz type Genocchi zeta function, and q -Genocchi type l -function. We define partial zeta function. By using this function, we construct p -adic interpolation functions which interpolate generalized q -Genocchi numbers at negative integers. We also define p -adic meromorphic functions on C p . Furthermore, we construct new generating 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 these sums.