# The Values of the Riemann Zeta-Function on Discrete Sets

Source: [The Values of the Riemann Zeta-Function on Discrete Sets](<https://www.sota2.com/research/paper/68fa587a1e209131ce9aeb58>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:21:36.715Z

Authors: Junghun Lee, Athanasios Sourmelidis, J\\"orn Steuding, Ade Irma Suriajaya

Published: 2017-10-31T08:16:43.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1710.11367>)

[PDF](<https://arxiv.org/pdf/1710.11367.pdf>)