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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

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

Rights: Copyright © 2020 Mathematical Society of Japan

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