Twisted p-adic .h; q/-L-functions

By using the q-Volkenborn integral on Zp, 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 D 0. We also find the residue of this function at s D 1. We construct a p-adic twisted .h; q/-L-function which interpolates the twisted .h; q/-Bernoulli polynomials: L.h/ ;p;q.1 􀀀 n; t; / D 􀀀 B.h/ n; n; .p t; q/ 􀀀 n.p/pn􀀀1B.h/ n; n;1.p􀀀1p t; qp/ 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.