منابع مشابه
On the Mean Values of Dirichlet L-functions
Abstract. We study the 2k-th power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes and Keating for the Riemann zeta-function. This allows us to recover conjectures for the moments based on random matrix models, inc...
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Let f(n) be a totally multiplicative function such that |f(n)| ≤ 1 for all n, and let F (s) = ∑∞ n=1 f(n)n−s be the associated Dirichlet series. A variant of Halász’s method is developed, by means of which estimates for ∑N n=1 f(n)/n are obtained in terms of the size of |F (s)| for s near 1 with 1. The result obtained has a number of consequences, particularly concerning the zeros of the p...
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Introduction Let p be a prime number. In this note, we combine the methods of Hida with the results of [HK1] to define a p-adic analytic function, the squares of whose special values are related to the values of triple product L-functions at their centers of symmetry. More precisely, let f , g, and h be classical normalized cuspidal Hecke eigenforms of level 1 and (even) weights k, l, and m, re...
متن کاملFunctional Relations and Special Values of Mordell-tornheim Triple Zeta and L-functions
In this paper, we prove the existence of meromorphic continuation of certain triple zeta-functions of Lerch’s type. Based on this result, we prove some functional relations for triple zeta and L-functions of the MordellTornheim type. Using these functional relations, we prove new explicit evaluation formulas for special values of these functions. These can be regarded as triple analogues of kno...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2015
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-015-0841-5