منابع مشابه
p-ADIC DEDEKIND AND HARDY-BERNDT TYPE SUMS RELATED TO VOLKENBORN INTEGRAL ON Zp
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 ...
متن کاملOn p-adic q-L-functions and sums of powers
Let p be a fixed prime. Throughout this paper Zp, Qp, C and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp, cf.[1, 4, 6, 10]. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = p. When one talks of q-extension, q is variously considered as an...
متن کاملp-ADIC q-EXPANSION OF ALTERNATING SUMS OF POWERS
Let p be a fixed prime. Throughout this paper Zp, Qp, C and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp, cf.[1, 4, 6, 10]. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = p. When one talks of q-extension, q is variously considered as an...
متن کاملSharp estimates for the p-adic Hardy type operators on higher-dimensional product spaces
In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spa...
متن کاملq-HARDY-BERNDT TYPE SUMS ASSOCIATED WITH q-GENOCCHI TYPE ZETA AND l-FUNCTIONS
Abstract. The aim of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function, q-analogue Genocchi type l-function and two-variable qGenocchi type l-function. Furthermore, we construct new genereting functions of q-Hardy-Berndt type...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2006
ISSN: 0304-9914
DOI: 10.4134/jkms.2006.43.1.111