{
  "id": "1303.2329",
  "version": "v8",
  "published": "2013-03-10T15:10:03.000Z",
  "updated": "2017-08-11T16:26:06.000Z",
  "title": "New Results for Sorli's Conjecture on Odd Perfect Numbers - Part II",
  "authors": [
    "Jose Arnaldo B. Dris"
  ],
  "comment": "14 pages (withdrawn because of a crucial gap in Theorem 1 [see arXiv:1309.0906 for what is currently provable in this regard], as well as elementary mistakes in the numerical bounds from pages 2 to 4)",
  "categories": [
    "math.NT"
  ],
  "abstract": "If $N={q^k}{n^2}$ is an odd perfect number given in Eulerian form, then Sorli's conjecture predicts that $k=\\nu_{q}(N)=1$. In this article, we give some further results related to this conjecture and those contained in the papers \\cite{Dris} and \\cite{Dris2}. (withdrawn because of a crucial gap in Theorem 1 [see https://arxiv.org/pdf/1309.0906.pdf for what is currently provable in this regard], as well as elementary mistakes in the numerical bounds from pages 2 to 4)",
  "revisions": [
    {
      "version": "v7",
      "updated": "2013-08-14T07:40:15.000Z",
      "abstract": "If $N={q^k}{n^2}$ is an odd perfect number given in Eulerian form, then Sorli's conjecture predicts that $k=\\nu_{q}(N)=1$. In this article, we give some further results related to this conjecture and those contained in the papers \\cite{Dris} and \\cite{Dris2}.",
      "comment": "14 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v8",
      "updated": "2017-08-11T16:26:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11J25",
      "11J99"
    ],
    "keywords": [
      "odd perfect number",
      "sorlis conjecture predicts",
      "eulerian form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.2329D"
    }
  }
}