Twisted pp-adic (h,q)(h,q)-LL-functions

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