Towards a statistical proof of the Riemann Hypothesis

Details Towards a statistical proof of the Riemann Hypothesis Towards a statistical proof of the Riemann Hypothesis

2009-03-25

arxiv.org/abs/0903.4227v3

Mathematics

General Mathematics

9 pages, 1 figure. Revised because of an error on page 9

Scientific paper

Using the $\zeta$ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the $\zeta$ zeros is established. We then demonstrate that on the critical line, $|\zeta|$ is convex, and that in the region $0 < \Re(s) \leq 0.5$, $|\zeta|$ 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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