Discrete Ω-results for the Riemann zeta function-Reference-Cited by-同舟云学术

Discrete Ω-results for the Riemann zeta function

Published:2024-09-03 Issue: Volume: Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Minelli Paolo¹^ORCID,Sourmelidis Athanasios²^ORCID

Affiliation:

1. Department of Mathematics , KTH Royal Institute of Technology , Stockholm , Sweden

2. Insitute for Analysis and Number Theory , 27253 Graz University of Technology , Steyrergasse 30, 8010 Graz , Austria

Abstract

Abstract We study lower bounds for the Riemann zeta function ζ ⁢ ( s )

{\zeta(s)}

along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the exponential, with the ones known for the continuous case, that is when the imaginary part of s ranges on a given interval. Our methods are based on a discretization of the resonance method for estimating extremal values of ζ ⁢ ( s )

{\zeta(s)}

Funder

Austrian Science Fund

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2023-0324/pdf

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