Discrete Universality in the Selberg Class |
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Authors: | A. Laurinčikas R. Macaitienė |
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Affiliation: | 1.Faculty of Mathematics and Informatics,Vilnius University,Vilnius,Lithuania;2.?iauliai University,?iauliai,Lithuania;3.?iauliai State College,?iauliai,Lithuania |
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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 + iτ ), 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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