{
  "id": "1311.6180",
  "version": "v3",
  "published": "2013-11-24T22:33:06.000Z",
  "updated": "2015-11-26T17:17:02.000Z",
  "title": "Moderate and Large Deviations for the Erdős-Kac Theorem",
  "authors": [
    "Behzad Mehrdad",
    "Lingjiong Zhu"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR",
    "math.NT"
  ],
  "abstract": "The Erd\\H{o}s-Kac theorem is a celebrated result in number theory which says that the number of distinct prime factors of a uniformly chosen random integer satisfies a central limit theorem. In this paper, we establish the large deviations and moderate deviations for this problem in a very general setting for a wide class of additive functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-08T22:18:06.000Z",
      "title": "Moderate and Large Deviations for Erdős-Kac Theorem",
      "abstract": "Erd\\H{o}s-Kac theorem is a celebrated result in number theory which says that the number of distinct prime factors of a uniformly chosen random integer satisfies a central limit theorem. In this paper, we establish the large deviations and moderate deviations for this problem in a very general setting for a wide class of additive functions.",
      "comment": "12 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-11-26T17:17:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviations",
      "erdős-kac theorem",
      "uniformly chosen random integer satisfies",
      "distinct prime factors",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6180M"
    }
  }
}