On the zeros of Riemann's zeta-function on the critical line

By Siegfred Baluyot. 2016

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Abstract We combine the mollifier method with a zero detection method of Atkinson to prove in a new way that a positive proportion of the nontrivial zeros of the Riemann zeta-function ζ ( s ) are on the critical line. One of the main ingredients of the proof is an estimate for a mollified fourth moment of ζ ( s ) . We deduce this estimate from the twisted fourth moment formula that has been recently developed by Hughes and Young.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f1be9da3d9be23b049cf7de57e9466e8180730bf