The Maximum of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis

Helmut Maier (), Michael Th. Rassias () and Andrei Raigorodskii ()
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Helmut Maier: University of Ulm, Department of Mathematics
Michael Th. Rassias: University of Zurich, Institute of Mathematics
Andrei Raigorodskii: Moscow Institute of Physics and Technology

A chapter in Trigonometric Sums and Their Applications, 2020, pp 149-158 from Springer

Abstract: Abstract In a previous paper (see H. Maier, M. Th. Rassias, The maximum of cotangent sums related to Estermann’s zeta function in rational numbers in short intervals. Appl. Anal. Discrete Math. 11, 166–176 (2017)) we investigate the maximum of certain cotangent sums. These cotangent sums can be associated to the study of the Riemann Hypothesis through its relation with the so-called Vasyunin sum. Here we continue this research by restricting the rational numbers in short intervals to rational numbers of special type.

Keywords: Cotangent sums; Estermann zeta function; Nyman-Beurling criterion; Riemann zeta function; Riemann Hypothesis; 26A12; 11L03. (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/978-3-030-37904-9_7

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