On the Discrete Approximation by the Mellin Transform of the Riemann Zeta-Function

Virginija Garbaliauskienė, Antanas Laurinčikas and Darius Šiaučiūnas ()
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Virginija Garbaliauskienė: Faculty of Business and Technologies, Šiauliai State University of Applied Sciences, Aušros av. 40, LT-76241 Šiauliai, Lithuania
Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
Darius Šiaučiūnas: Institute of Regional Development, Šiauliai Academy, Vilnius University, P. Višinskio str. 25, LT-76351 Šiauliai, Lithuania

Mathematics, 2023, vol. 11, issue 10, 1-15

Abstract: In the paper, it is obtained that there are infinite discrete shifts Ξ ( s + i k h ) , h > 0 , k ∈ N 0 of the Mellin transform Ξ ( s ) of the square of the Riemann zeta-function, approximating a certain class of analytic functions. For the proof, a probabilistic approach based on weak convergence of probability measures in the space of analytic functions is applied.

Keywords: discrete limit theorem; Mellin transform; Riemann zeta-function; weak convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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