Discrete Approximation by a Dirichlet Series Connected to the Riemann Zeta-Function

Antanas Laurinčikas and Darius Šiaučiūnas
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Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
Darius Šiaučiūnas: Regional Development Institute, Šiauliai Academy, Vilnius University, P. Višinskio Str. 25, LT-76351 Šiauliai, Lithuania

Mathematics, 2021, vol. 9, issue 10, 1-11

Abstract: In the paper, a Dirichlet series ? u N ( s ) whose shifts ? u N ( s + i k h ) , k = 0 , 1 , ? , h > 0 , approximate analytic non-vanishing functions defined on the right-hand side of the critical strip is considered. This series is closely connected to the Riemann zeta-function. The sequence u N ? ? and u N ? N 2 as N ? ? .

Keywords: distribution function; Riemann zeta-function; Voronin universality theorem; weak convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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