p-ADIC DEDEKIND AND HARDY-BERNDT TYPE SUMS RELATED TO VOLKENBORN INTEGRAL ON Zp
نویسنده
چکیده
where ((x)) = x − [x]G − 1 2 , if x / ∈ Z, ((x)) = 0, x ∈ Z, where [x]G is the largest integer ≤ x cf. ([1], [5], [9], [11], [12], [13]). In this paper, Zp, Qp, Cp, C and Z, respectively, denote the ring of p-adic integers, the field of p-adic rational numbers, the p-adic completion of the algebraic closure of Qp normalized by |p|p = p −1, and the complex field and integer numbers. Let q be an indeterminate such that if q ∈ C, then |q| < 1 and if q ∈ Cp, then |1− q|p < p −1/(p−1), so that qx =exp `
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