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

Stefano Beltraminelli·Danilo Merlini
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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.

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Stefano Beltraminelli, Danilo Merlini. 2006-01-07. The criteria of Riesz, Hardy-Littlewood et al. for the Riemann Hypothesis revisited using similar functions. https://arxiv.org/abs/math/0601138

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