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Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function

Mossinghoff, M; Trudgian, Timothy


We prove that the Riemann zeta-function ζ(σ + it) has no zeros in the region σ ≥ 1 − 1/(5.573412 log |t|) for |t| ≥ 2. This represents the largest known zero-free region within the critical strip for 3.06 · 1010 < |t| < exp(10 151.5). Our improvements result from determining some favorable trigonometric polynomials having particular properties, and from analyzing the error term in the method of Kadiri. We also improve an upper bound in a question of Landau regarding nonnegative trigonometric...[Show more]

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
Source: Journal of Number Theory
DOI: 10.1016/j.jnt.2015.05.010


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