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arXiv · 0810.4820

Densities, Laplace Transforms and Analytic Number Theory

Sibusiso Sibisi
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Abstract

Li showed that the Riemann Hypothesis is equivalent to the nonnegativity of a certain sequence of numbers. Bombieri and Lagarias gave an arithmetic formula for the number sequence based on the Guinand-Weil explicit formula and showed that Li's criterion is equivalent to Weil's criterion for the Riemann Hypothesis. We provide a derivation of the explicit formula based on Laplace transforms and present an alternative expression for Li's criterion that invites a probabilistic interpretation.

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Sibusiso Sibisi. 2008-10-27. Densities, Laplace Transforms and Analytic Number Theory. https://arxiv.org/abs/0810.4820

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