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

Author

Listed:
  • Virginija Garbaliauskienė

    (Faculty of Business and Technologies, Šiauliai State University of Applied Sciences, Aušros av. 40, LT-76241 Šiauliai, Lithuania
    These authors contributed equally to this work.)

  • Antanas Laurinčikas

    (Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Darius Šiaučiūnas

    (Institute of Regional Development, Šiauliai Academy, Vilnius University, P. Višinskio str. 25, LT-76351 Šiauliai, Lithuania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Virginija Garbaliauskienė & Antanas Laurinčikas & Darius Šiaučiūnas, 2023. "On the Discrete Approximation by the Mellin Transform of the Riemann Zeta-Function," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2315-:d:1147963
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