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

Helmut Maier; Michael Th. Rassias

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.

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Helmut Maier. Michael Th. Rassias. "On the maximum of cotangent sums related to the Riemann hypothesis in rational numbers in short intervals." Mosc. J. Comb. Number Theory 10 (4) 303 - 313, 2022. https://doi.org/10.2140/moscow.2021.10.303

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Received: 1 August 2021; Accepted: 17 December 2021; Published: 2022

First available in Project Euclid: 17 February 2022

MathSciNet: MR4366117

Digital Object Identifier: 10.2140/moscow.2021.10.303

Subjects:

Primary: 11L03 , 11M06 , 26A12

Keywords: cotangent sums , Estermann’s zeta function , Kloosterman sums , Nyman–Beurling criterion , Riemann hypothesis , Riemann zeta function

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