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

2014/10/15 by Mossinghoff, Michael J., Trudgian, Timothy S. · 3 citations
#11M26 #11Y35 #42A05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1410.3926

Abstract

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|

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