Proceedings of the Steklov Institute of Mathematics

, Volume 299, Issue 1, pp 143–156 | Cite as

Discrete Universality in the Selberg Class

Article

Abstract

The Selberg class S consists of functions L(s) that are defined by Dirichlet series and satisfy four axioms (Ramanujan conjecture, analytic continuation, functional equation, and Euler product). It has been known that functions in S that satisfy the mean value condition on primes are universal in the sense of Voronin, i.e., every function in a sufficiently wide class of analytic functions can be approximated by the shifts L(s + ), τ ∈ R. In this paper we show that every function in the same class of analytic functions can be approximated by the discrete shifts L(s + ikh), k = 0, 1,..., where h > 0 is an arbitrary fixed number.

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Šiauliai UniversityŠiauliaiLithuania
  3. 3.Šiauliai State CollegeŠiauliaiLithuania

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