q-Hardy–Berndt type sums associated with q-Genocchi type zeta and q-l-functions Original Research Article

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 qq-analogue of the Genocchi zeta function, qq-analogue Hurwitz type Genocchi zeta function, and qq-Genocchi type ll-function. We define partial zeta function. By using this function, we construct pp-adic interpolation functions which interpolate generalized qq-Genocchi numbers at negative integers. We also define pp-adic meromorphic functions on CpCp. Furthermore, we construct new generating functions of qq-Hardy–Berndt type sums and qq-Hardy–Berndt type sums attached to Dirichlet character. We also give some new relations, related to these sums.