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Zeros of the Riemann zeta-function and its universality

Volume 181 / 2017

Ramūnas Garunkštis, Antanas Laurinčikas, Renata Macaitienė Acta Arithmetica 181 (2017), 127-142 MSC: Primary 11M06. DOI: 10.4064/aa8583-5-2017 Published online: 17 November 2017

Abstract

Let $0 \lt \gamma_1\leq \gamma_2 \leq\cdots$ be the imaginary parts of non-trivial zeros of the Riemann zeta-function $\zeta(s)$. Using the Montgomery conjecture (its weaker form) on the pair correlation of the sequence $\{\gamma_k\}$, we show that analytic functions of a wide class can be approximated by shifts $\zeta(s+i\gamma_k)$.

Authors

  • Ramūnas GarunkštisFaculty of Mathematics and Informatics
    Vilnius University
    Naugarduko St. 24
    LT-03225 Vilnius, Lithuania
    e-mail
  • Antanas LaurinčikasFaculty of Mathematics and Informatics
    Vilnius University
    Naugarduko St. 24
    LT-03225 Vilnius, Lithuania
    e-mail
  • Renata MacaitienėResearch Institute
    Šiauliai University
    P. Višinskio St. 25
    LT-76351 Šiauliai, Lithuania
    e-mail

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