Vol. 10, No. 4, 2021

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On the maximum of cotangent sums related to the Riemann hypothesis in rational numbers in short intervals

Helmut Maier and Michael Th. Rassias

Vol. 10 (2021), No. 4, 303–313
DOI: 10.2140/moscow.2021.10.303
Abstract

Cotangent sums play a significant role in the Nyman–Beurling criterion for the Riemann hypothesis. Here we investigate the maximum of the values of these cotangent sums over various sets of rational numbers in short intervals.

Keywords
cotangent sums, Estermann's zeta function, Riemann zeta function, Riemann hypothesis, Kloosterman sums, Nyman–Beurling criterion
Mathematical Subject Classification
Primary: 11L03, 11M06, 26A12
Milestones
Received: 1 August 2021
Accepted: 17 December 2021
Published: 17 January 2022
Authors
Helmut Maier
Department of Mathematics
University of Ulm
Ulm
Germany
Michael Th. Rassias
Department of Mathematics and Engineering Sciences
Hellenic Military Academy
Athens
Greece
Moscow Institute of Physics and Technology
Dolgoprudny
Russia
Program in Interdisciplinary Studies
Institute for Advanced Study
Princeton, NJ
United States