Work

Discrete Ω-results for the Riemann zeta function

Year: 2024

Type: article

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)} .

Source: Forum Mathematicum

DOI: 10.1515/forum-2023-0324

Authors: Paolo Minelli, Athanasios Sourmelidis

Institutions: KTH Royal Institute of Technology, Graz University of Technology

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Austrian Science Fund

Awards: G2340322753, Value Distribution of Zeta- and L-Functions, Geometry of Numbers and Diophantine Approximation