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

Author

Listed:
  • 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

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

Abstract

In the paper, a Dirichlet series ζ u N ( s ) whose shifts ζ 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 → ∞ .

Suggested Citation

  • Antanas Laurinčikas & Darius Šiaučiūnas, 2021. "Discrete Approximation by a Dirichlet Series Connected to the Riemann Zeta-Function," Mathematics, MDPI, vol. 9(10), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1073-:d:551815
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