{
  "id": "0810.4820",
  "version": "v1",
  "published": "2008-10-27T15:09:04.000Z",
  "updated": "2008-10-27T15:09:04.000Z",
  "title": "Densities, Laplace Transforms and Analytic Number Theory",
  "authors": [
    "Sibusiso Sibisi"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-27T15:09:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M36",
      "60E07"
    ],
    "keywords": [
      "analytic number theory",
      "laplace transforms",
      "riemann hypothesis",
      "lis criterion",
      "guinand-weil explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4820S"
    }
  }
}