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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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