A new approach to q-zeta function
نویسنده
چکیده
Throughout this paper Z,Zp,Qp and Cp will be denoted by the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp, respectively, cf. [7, 8, 9, 10]. Let νp be the normalized exponential valuation of Cp with |p|p = p −νp(p) = p. When one talks of qextension, q is variously considered as an indeterminate, a complex number q ∈ C, or p-adic number q ∈ Cp. If q ∈ Cp, then we normally assume |q − 1|p < p − 1 p−1 , so that q = exp(x log q) for |x|p ≤ 1. If q ∈ C, then we normally assume that |q| < 1. For f ∈ UD(Zp,Cp) = {f |f : Zp → Cp is uniformly differentiable function}, the p-adic qintegral (or q-Volkenborn integration) was defined as
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