Twisted p-adic (h,q)-L-functions

TL;DR

This paper introduces new twisted (h,q)-L-functions using q-Volkenborn integrals, Mellin transforms, and p-adic methods, providing integral representations, interpolation properties, and special value calculations.

Contribution

It constructs novel twisted (h,q)-L-functions and related zeta functions, offering new integral representations and interpolation results in the p-adic setting.

Findings

Constructed integral representations of twisted (h,q)-L-functions.

Derived values and residues at special points s=0 and s=1.

Established interpolation of twisted (h,q)-Bernoulli polynomials.

Abstract

By using q-Volkenborn integral on Z_{p}, we (simsek, simsekCanada) constructed new generating functions of the (h,q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to the generating functions, we constructed integral representation of the twisted (h,q)-Hurwitz function and twisted (h,q)-two-variable L-function. By using these functions, we construct twisted new (h,q)-partial zeta function which interpolates the twisted (h,q)-Bernoulli polynomials and generalized twisted (h,q)-Bernoulli numbers at negative integers. We give relation between twisted (h,q)-partial zeta functions and twisted (h,q)-two-variable L-function. We find the value of this function at s=0. We also find residue of this function at s=1. We construct p-adic twisted (h,q)-L-function, which interpolates the twisted (h,q)-Bernoulli polynomials.