{
  "id": "1607.08521",
  "version": "v1",
  "published": "2016-07-22T12:26:44.000Z",
  "updated": "2016-07-22T12:26:44.000Z",
  "title": "The $β$-functions and their relation to the prime counting function",
  "authors": [
    "Dimitris Vartziotis",
    "Aristos Tzavellas"
  ],
  "comment": "10 pages, 6 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "We introduce the arithmetic $\\beta$-functions and investigate the asymptotic behaviour of $$\\frac{\\sum\\limits_{n \\leq x} \\beta(n)}{x}$$ in relation to the prime counting function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-22T12:26:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37"
    ],
    "keywords": [
      "prime counting function",
      "asymptotic behaviour",
      "arithmetic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}