{
  "id": "1307.5723",
  "version": "v7",
  "published": "2013-07-22T14:18:27.000Z",
  "updated": "2014-06-19T11:23:04.000Z",
  "title": "Some sums over the non-trivial zeros of the Riemann zeta function",
  "authors": [
    "Jesús Guillera"
  ],
  "comment": "Improved version. (17 pages)",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove some identities, which involve the non-trivial zeros of the Riemann zeta function. From them we derive some convergent asymptotic expansions related to the work by Cram\\'er, and also new representations for some arithmetical functions in terms of the non-trivial zeros.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2014-06-19T11:23:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "non-trivial zeros",
      "convergent asymptotic expansions",
      "identities",
      "representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.5723G"
    }
  }
}