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arXiv · 1710.11367

The Values of the Riemann Zeta-Function on Discrete Sets

Junghun Lee·Athanasios Sourmelidis·Jörn Steuding·Ade Irma Suriajaya
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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 $\zeta$.

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Junghun Lee, Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya. 2017-10-31. The Values of the Riemann Zeta-Function on Discrete Sets. https://doi.org/10.2969/aspm%2F08410315

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