Densities, Laplace Transforms and Analytic Number Theory

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dc.creatorSibisi, Sibusiso
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:13:25Z
dc.date.available2026-07-07T10:13:25Z
dc.descriptionLi 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.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0810.4820
dc.identifierhttp://arxiv.org/abs/0810.4820
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172524
dc.subjectNumber Theory
dc.subject11M36 (Primary) 60E07 (Secondary)
dc.titleDensities, Laplace Transforms and Analytic Number Theory
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