{
  "id": "1907.11994",
  "version": "v1",
  "published": "2019-07-28T00:26:37.000Z",
  "updated": "2019-07-28T00:26:37.000Z",
  "title": "Large prime gaps and progressions with few primes",
  "authors": [
    "Kevin Ford"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that the existence of arithmetic progressions with few primes, with a quantitative bound on ``few'', implies the existence of larger gaps between primes less than x than is currently known unconditionally. In particular, we derive this conclusion if there are certain types of exceptional zeros of Dirichlet L-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-28T00:26:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11N13",
      "11M20"
    ],
    "keywords": [
      "large prime gaps",
      "arithmetic progressions",
      "dirichlet l-functions",
      "larger gaps",
      "exceptional zeros"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}