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

Abstract

By using the q -Volkenborn integral on Z p , in Simsek (2006) [33] and Simsek (2007) [34] , generating functions for the ( h , q ) -Bernoulli polynomials and numbers were defined. By using these functions, we define a new twisted ( 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 a relation between twisted ( h , q ) -partial zeta functions and the twisted ( h , q ) -two-variable L -function. We find the value of this function at s = 0 . We also find the residue of this function at s = 1 . We construct a p -adic twisted ( h , q ) - L -function which interpolates the twisted ( h , q ) -Bernoulli polynomials: L ξ , p , q ( h ) ( 1 − n , t , χ ) = − B n , χ n , ξ ( h ) ( p ∗ t , q ) − χ n ( p ) p n − 1 B n , χ n , 1 ( h ) ( p − 1 p ∗ t , q p ) n . Furthermore, we construct an integral representation of the twisted ( h , q ) -two-variable L -function. We give some applications related to the p -adic twisted ( h , q ) - L -function and the twisted ( h , q ) -Bernoulli polynomials.