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

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.

13 pages

References in corpus (6)

• $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
• Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
• A New approach to q-zeta function
• On the twisted $q$-zeta functions and $q$-Bernoulli polynomials
• On the two-variable Dirichlet q-L-series
• On a p-adic interpolation function for the q-extension of the generalized Bernoulli polynomials and Its derivative

Cited by in corpus (3)

• Explicit formulas for p-adic integrals: approach to p-adic distributions and some families of special numbers and polynomials
• Identities on the k-ary Lyndon words related to a family of zeta functions
• Some new identities on the twisted (h, q)- Euler numbers and q-Bernstein polynomials