{
  "id": "1205.5021",
  "version": "v1",
  "published": "2012-05-22T19:47:19.000Z",
  "updated": "2012-05-22T19:47:19.000Z",
  "title": "3-tuples have at most 7 prime factors infinitely often",
  "authors": [
    "James Maynard"
  ],
  "comment": "13 Pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $L_1$, $L_2$ $L_3$ be integer linear functions with no fixed prime divisor. We show there are infinitely many $n$ for which the product $L_1(n)L_2(n)L_3(n)$ has at most 7 prime factors, improving a result of Porter. We do this by means of a weighted sieve based upon the Diamond-Halberstam-Richert multidimensional sieve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-22T19:47:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11N35",
      "11N36"
    ],
    "keywords": [
      "prime factors",
      "diamond-halberstam-richert multidimensional sieve",
      "integer linear functions",
      "fixed prime divisor"
    ],
    "publication": {
      "doi": "10.1017/S0305004113000339",
      "journal": "Mathematical Proceedings of the Cambridge Philosophical Society",
      "year": 2013,
      "month": "Nov",
      "volume": 155,
      "number": 3,
      "pages": 443
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013MPCPS.155..443M"
    }
  }
}