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 کاملReal zeros of real odd Dirichlet L-functions
Let χ be a real odd Dirichlet character of modulus d, and let L(s, χ) be the associated Dirichlet L-function. As a consequence of the work of Low and Purdy, it is known that if d ≤ 800 000 and d 6= 115 147, 357 819, 636 184, then L(s, χ) has no positive real zeros. By a simple extension of their ideas and the advantage of thirty years of advances in computational power, we are able to prove tha...
متن کاملJulia Lines of General Random Dirichlet Series
In this paper, we consider a random entire function f(s, ω) defined by a random Dirichlet series ∑∞ n=1Xn(ω)e −λns whereXn are independent and complex valued variables, 0 6 λn ր +∞. We prove that under natural conditions, for some random entire functions of order (R) zero f(s, ω) almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J....
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2019
ISSN: 1083-589X
DOI: 10.1214/19-ecp260