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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 |
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Vol. 10 (2021), No. 4, 303–313
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DOI: 10.2140/moscow.2021.10.303
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Abstract |
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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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Keywords
cotangent sums, Estermann's zeta function, Riemann zeta
function, Riemann hypothesis, Kloosterman sums,
Nyman–Beurling criterion
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Mathematical Subject Classification
Primary: 11L03, 11M06, 26A12
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Milestones
Received: 1 August 2021
Accepted: 17 December 2021
Published: 17 January 2022
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Authors |
| Helmut Maier | ||
| Department of Mathematics University of Ulm Ulm Germany |
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| 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 |
