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

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.

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