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VOL. 84 | 2020 The values of the Riemann zeta-function on discrete sets
Junghun Lee, Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya

Editor(s) Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki

Adv. Stud. Pure Math., 2020: 315-334 (2020) DOI: 10.2969/aspm/08410315

Abstract

We study the values taken by the Riemann zeta-function $\zeta$ on discrete sets. We show that infinite vertical arithmetic progressions are uniquely determined by the values of $\zeta$ taken on this set. Moreover, we prove a joint discrete universality theorem for $\zeta$ with respect to certain permutations of the set of positive integers. Finally, we study a generalization of the classical denseness theorems for $\zeta$.

Information

Published: 1 January 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07283190

Digital Object Identifier: 10.2969/aspm/08410315

Subjects:
Primary: 11M06

Keywords: Riemann zeta-function , Universality , value-distribution

Rights: Copyright © 2020 Mathematical Society of Japan

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