منابع مشابه
Uniform Distribution of Zeros of Dirichlet Series
We consider a class of Dirichlet series which is more general than the Selberg class. Dirichlet series in this class, have meromorphic continuation to the whole plane and satisfy a certain functional equation. We prove, under the assumption of a certain hypothesis concerning the density of zeros on average, that the sequence formed by the imaginary parts of the zeros of a Dirichlet series in th...
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Let a = (an)n≥1 be a periodic sequence, Fa(s) the meromorphic continuation of P n≥1 an/n , and Na(σ1, σ2, T ) the number of zeros of Fa(s), counted with their multiplicities, in the rectangle σ1 < Re s < σ2, | Im s| ≤ T . We extend previous results of Laurinčikas, Kaczorowski, Kulas, and Steuding, by showing that if Fa(s) is not of the form P (s)Lχ(s), where P (s) is a Dirichlet polynomial and ...
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A small part of the Generalized Riemann Hypothesis asserts that L-functions do not have zeros on the line segment ( 2 , 1]. The question of vanishing at s = 2 often has deep arithmetical significance, and has been investigated extensively. A persuasive view is that L-functions vanish at 2 either for trivial reasons (the sign of the functional equation being negative), or for deep arithmetical r...
متن کاملZeros of Functions with Finite Dirichlet Integral
In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral. This is a remark about the zeros of functions f = ), n�0 anz holomorphic on U z z < 1} that have finite Dirichlet integral D(f ) := ∞ |f |dA = n|an|, n=0 where dA is Lebesgue measure in the plane. Clearly such functions belong to th...
متن کاملOn the zeros of the Ramanujan tau-Dirichlet series in the critical strip
We describe computations which show that each of the first 12069 zeros of the Ramanujan τ -Dirichlet series of the form σ + it in the region 0 < t < 6397 is simple and lies on the line σ = 6. The failures of Gram’s law in this region are also noted. The first 5018 zeros and 2228 successive zeros beginning with the 20001st zero are also calculated. The distribution of the normalized spacing of t...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2015
ISSN: 0019-3577
DOI: 10.1016/j.indag.2015.09.007