$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
Abstract
By using -Volkenborn integration and uniform differentiable on , we construct -adic -zeta functions. These functions interpolate the -Bernoulli numbers and polynomials. The value of -adic -zeta functions at negative integers are given explicitly. We also define new generating functions of -Bernoulli numbers and polynomials. By using these functions, we prove analytic continuation of some basic (or -) % -series. These generating functions also interpolate Barnes' type Changhee -Bernoulli numbers with attached to Dirichlet character as well. By applying Mellin transformation, we obtain relations between Barnes' type % -zeta function and new Barnes' type Changhee -Bernolli numbers. Furthermore, we construct the Dirichlet type Changhee (or -) % -functions.
Cite
@article{arxiv.math/0502019,
title = {$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series},
author = {T. Kim and Y. Simsek and H. M. Srivastav},
journal= {arXiv preprint arXiv:math/0502019},
year = {2007}
}
Comments
37 pages