2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107424The original criteria of Riesz and of Hardy-Littlewood concerning the truth of the Riemann Hypothesis (RH) are revisited and further investigated in light of the recent formulations and results of Maslanka and of Baez-Duarte concerning a representation of the Riemann Zeta function. Then we introduce a general set of similar functions with the emergence of Poisson-like distributions and we present some numerical experiments which indicate that the RH may barely be true.Submitted to: J. Phys. A: Math. GenNumber TheoryMathematical Physics11M26text