THE CRITERIA OF RIESZ, HARDY-LITTLEWOOD ET AL. FOR THE RIEMANN HYPOTHESIS REVISITED USING SIMILAR FUNCTIONS

Abstract

The 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.