$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series

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dc.creatorKim, T.
dc.creatorSimsek, Y.
dc.creatorSrivastav, H. M.
dc.date2005-02-01
dc.date.accessioned2026-07-07T05:16:35Z
dc.date.available2026-07-07T05:16:35Z
dc.descriptionBy 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.
dc.description37 pages
dc.identifierhttps://arxiv.org/abs/math/0502019
dc.identifierhttp://arxiv.org/abs/math/0502019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74039
dc.subjectNumber Theory
dc.subject11B68, 11S40, 33D05
dc.title$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
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