Twisted p p -adic (h,q) ( h , q ) -L L -functions
By using the q q -Volkenborn integral on Zp Z p , 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 L L -function. We find the value of this function at s=0 s = 0 . We also find the residue of this function at s=1 s = 1 . We construct a p p -adic twisted (h,q) ( h , q ) -L L -function which interpolates the twisted (h,q) ( h , q ) -Bernoulli polynomials:
q q -bernoulli numbers and polynomials q q q q q twisted q q -bernoulli numbers and polynomials q q q q q q q -zeta function q q q q q p p -adic l l -function p p p p p l l l l l twisted q q -zeta function q q q q q twisted q q -l l -function q q q q q l l l l l q q -volkenborn integral q q q q q