Gram Points in the Universality of the Dirichlet Series with Periodic Coefficients

Darius Šiaučiūnas and Monika Tekorė ()
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Darius Šiaučiūnas: Institute of Regional Development, Šiauliai Academy, Vilnius University, Vytauto Str. 84, LT-76352 Šiauliai, Lithuania
Monika Tekorė: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania

Mathematics, 2023, vol. 11, issue 22, 1-14

Abstract: Let a = { a m : m ∈ N } be a periodic multiplicative sequence of complex numbers and L ( s ; a ) , s = σ + i t a Dirichlet series with coefficients a m . In the paper, we obtain a theorem on the approximation of non-vanishing analytic functions defined in the strip 1 / 2 < σ < 1 via discrete shifts L ( s + i h t k ; a ) , h > 0 , k ∈ N , where { t k : k ∈ N } is the sequence of Gram points. We prove that the set of such shifts approximating a given analytic function is infinite. This result extends and covers that of [Korolev, M.; Laurinčikas, A. A new application of the Gram points. Aequat. Math. 2019 , 93 , 859–873]. For the proof, a limit theorem on weakly convergent probability measures in the space of analytic functions is applied.

Keywords: space of analytic functions; approximation of analytic functions; universality; weak convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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