2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224887Using 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.9 pages, 1 figure. Revised because of an error on page 9General Mathematics11M06, 11M26text