{
  "id": "1801.06906",
  "version": "v1",
  "published": "2018-01-21T22:59:16.000Z",
  "updated": "2018-01-21T22:59:16.000Z",
  "title": "Summatory function of the number of prime factors",
  "authors": [
    "Xianchang Meng"
  ],
  "comment": "20 pages, 7 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the summatory function of the number of prime factors for integers $\\leq x$ over arithmetic progressions. Numerical experiments suggest that some arithmetic progressions consist more number of prime factors than others. Greg Martin conjectured that the difference of the summatory functions should attain a constant sign for all sufficiently large $x$. In this paper, we provide strong evidence for Greg Martin's conjecture. Moreover, we derive a general theorem for arithmetic functions from the Selberg class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-21T22:59:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "11N60",
      "11M36"
    ],
    "keywords": [
      "prime factors",
      "summatory function",
      "arithmetic progressions consist",
      "greg martins conjecture",
      "selberg class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}