ON A q-ANALOGUE OF THE p-ADIC GENERALIZED TWISTED L-FUNCTIONS AND p-ADIC q-INTEGRALS
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چکیده
منابع مشابه
ON A q-ANALOGUE OF THE p-ADIC GENERALIZED TWISTED L-FUNCTIONS AND p-ADIC q-INTEGRALS
The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using padic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim’s h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question ...
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In the recent paper, Kim-Rim have studied interesting twisted q-Euler numbers and polynomials. In [8], Kim-Rim suggested the question to find a q-analogue of the p-adic twisted (h, q)-l-function which interpolates generalized twisted (h, q)-Euler numbers attached to χ. This question is remained open. The purpose of this paper is to give the answer of the question.
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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...
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are known as the first kind Euler numbers cf. 1 . From the generating function of the first kind Euler numbers, we note that E0 1 and En − ∑n k 0 n k Ek for n ∈ N. The first few are 1,−1/2, 0, 1/4,−1/2, . . . and E2k 0 for k ∈ N. Those numbers play an important role in number theory. For example, the Euler zeta-function essentially equals an Euler numbers at nonpositive integer: ζE −m Em for m ...
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Recently, Cangul et al. [I.N. Cangul, H. Ozden and Y. Simsek, Generating functions of the (h, q) extension of twisted Euler polynomials and numbers, Acta Math. Hungar. 120(3) (2008), 281-299] constructed new generating functions of the twisted (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ. They also constructed the partially twisted (h, q)-zeta function. They suggeste...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2007
ISSN: 0304-9914
DOI: 10.4134/jkms.2007.44.1.001