101. q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series
- Author
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Hari M. Srivastava, Kim, T., and Simsek, Y.
- Subjects
Mathematics - Number Theory ,11B68, 11S40, 33D05 ,Mathematics::Number Theory ,FOS: Mathematics ,Number Theory (math.NT) - Abstract
By using $q$-Volkenborn integration and uniform differentiable on $\mathbb{Z}%_{p}$, we construct $p$-adic $q$-zeta functions. These functions interpolate the $q$-Bernoulli numbers and polynomials. The value of $p$-adic $q$-zeta functions at negative integers are given explicitly. We also define new generating functions of $q$-Bernoulli numbers and polynomials. By using these functions, we prove analytic continuation of some basic (or $q$-) $L$% -series. These generating functions also interpolate Barnes' type Changhee $% q $-Bernoulli numbers with attached to Dirichlet character as well. By applying Mellin transformation, we obtain relations between Barnes' type $q$% -zeta function and new Barnes' type Changhee $q$-Bernolli numbers. Furthermore, we construct the Dirichlet type Changhee (or $q$-) $L$% -functions., 37 pages