The criteria of Riesz, Hardy-Littlewood et al. for the Riemann Hypothesis revisited using similar functions

Details The criteria of Riesz, Hardy-Littlewood et al. for the Riemann Hypothesis revisited using similar functions The criteria of Riesz, Hardy-Littlewood et al. for the Riemann Hypothesis revisited using similar functions

2006-01-07

arxiv.org/abs/math/0601138v1

Mathematics

Number Theory

Submitted to: J. Phys. A: Math. Gen

Scientific paper

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.

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