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

2007/11/01 by Yılmaz Şimşek, Yilmaz Simsek · 25 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics #Discrete mathematics #Function (biology) #Generating function #Mathematics #advanced mathematical theories #math.GM #math.NT #msc:11B68 #msc:11M99 #msc:11S40 #msc:11S80 #msc:30B50 #msc:44A05

paper · pdf · doi:10.1016/j.camwa.2009.12.015

published in Computers & Mathematics with Applications 59(6), 2097-2110 (Elsevier BV) · 13 pages

arxiv created 2007/11/01 · openalex publication_date 2010/01/09 · openalex created_date 2016/06/24 · arxiv updated 2018/11/19 · openalex updated_date 2026/08/05

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.

Citations

• 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
• On a p-adic interpolation function for the q-extension of the generalized Bernoulli polynomials and Its derivative