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On \(p\)-adic twisted \(q\)-\(L\)-functions related to generalized twisted Bernoulli numbers. (English) Zbl 1163.11312

Summary: In this paper, we construct a twisted \(q\)-partial zeta function and some twisted two-variable \(q\)-\(L\)-functions that interpolate \(q\)-Bernoulli numbers, \(\beta _{ n,\xi } ^{(h)} (q)\), and Bernoulli polynomials, \(\beta _{ n,x,\xi } ^{(h)} (x, q)\), respectively, at negative integers. Using these functions, we prove the existence of a \(p\)-adic interpolation function that interpolates the \(q\)-generalized polynomials \(\beta _{ n,x,\xi } ^{ (h) } (x, q)\) at negative integers. Consequently, we define a \(p\)-adic twisted \(q\)-\(L\)-function which is a solution of a question of T. Kim et al. [Far East J. Appl. Math. 13, No. 1, 13–21 (2003; Zbl 1046.11009)].

MSC:

11B65 Binomial coefficients; factorials; \(q\)-identities
11B68 Bernoulli and Euler numbers and polynomials
11S40 Zeta functions and \(L\)-functions
33D99 Basic hypergeometric functions

Citations:

Zbl 1046.11009
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References:

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