Densities, Laplace Transforms and Analytic Number Theory
Number Theory
2008-10-28 v1
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.
Cite
@article{arxiv.0810.4820,
title = {Densities, Laplace Transforms and Analytic Number Theory},
author = {Sibusiso Sibisi},
journal= {arXiv preprint arXiv:0810.4820},
year = {2008}
}
Comments
10 pages