منابع مشابه
On Mean Values of Dirichlet Polynomials
We show the following general lower bound valid for any positive integer q, and arbitrary reals φ1, . . . , φN and non-negative reals a1, . . . , aN , cq ( N ∑ n=1 a 2 n )q ≤ 1 2T ∫
متن کاملOn 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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In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of ...
متن کاملMean value theorems for long Dirichlet polynomials and tails of Dirichlet series
We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications b...
متن کاملOn certain mean values and the value-distribution of logarithms of Dirichlet L-functions
We study the value-distribution of Dirichlet L-functions L(s, χ) in the half-plane σ = 1/2. The main result is that a certain average of the logarithm of L(s, χ) with respect to χ, or of the Riemann zeta-function ζ(s) with respect to =s, can be expressed as an integral involving a density function, which depends only on σ and can be explicitly constructed. Several mean-value estimates on L...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2011
ISSN: 1331-4343
DOI: 10.7153/mia-14-45