The maximum of cotangent sums related to Estermann’s zeta function in rational numbers is short intervals

DOI10.2298/AADM1701166MzbMath1499.11255MaRDI QIDQ5034282

Helmut Maier, Michael Th. Rassias

Publication date: 24 February 2022

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

Riemann zeta functionKloosterman sumRiemann hypothesiscotangent sumsEstermann's zeta function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Trigonometric and exponential sums (general theory) (11L03) Rate of growth of functions, orders of infinity, slowly varying functions (26A12)

Related Items (6)

Cotangent Sums Related to the Riemann Hypothesis for Various Shifts of the Argument ⋮ Estimates of sums related to the Nyman-Beurling criterion for the Riemann hypothesis ⋮ On a Category of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis ⋮ The Maximum of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis ⋮ Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann hypothesis ⋮ On the maximum of cotangent sums related to the Riemann hypothesis in rational numbers in short intervals

Cites Work

• The rate of growth of moments of certain cotangent sums
• Period functions and cotangent sums
• The order of magnitude for moments for certain cotangent sums
• A generalization of Rademacher's reciprocity law
• On the Distribution of a Cotangent Sum: Fig. 1.
• The value of the Estermann zeta functions at s=0
• Asymptotics for moments of certain cotangent sums
• Generalizations of a cotangent sum associated to the Estermann zeta function
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