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arXiv · 0903.4227

Towards a statistical proof of the Riemann Hypothesis

Jon Breslaw
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Abstract

Using the $ζ$ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the $ζ$ zeros is established. We then demonstrate that on the critical line, $|ζ|$ is convex, and that in the region $0 < \Re(s) \leq 0.5$, $|ζ|$ has a negative slope, given the RH. In each case, analytical formulae are established, and numerical examples are presented to validate these formulae.

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Jon Breslaw. 2009-03-29. Towards a statistical proof of the Riemann Hypothesis. https://arxiv.org/abs/0903.4227

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