On the two-variable Dirichlet q-L-series

TL;DR

This paper introduces new two-variable q-L-functions that interpolate special polynomials and provides integral representations, advancing the understanding of q-analogs in number theory.

Contribution

It constructs two-variable multiple Dirichlet q-L-functions and Changhee q-L-functions, and derives their integral representations using Mellin transforms.

Findings

Defined new two-variable q-L-functions interpolating polynomials

Derived integral representations for these functions

Enhanced the theoretical framework of q-analogs in number theory

Abstract

In this study, we construct the two-variable multiple Dirichlet q-L-function and two-variable multiple Dirichlet type Changhee q-L-function. These functions interpolate the q-Bernoulli polynomials and generalized Changhee q-Bernoulli polynomials. By using the Mellin transformation, we give an integral representation for the two-variable multiple Dirichlet type q-zeta function and the two variable multiple Dirichlet type Changhee q-L-function.