{
  "id": "1211.4917",
  "version": "v2",
  "published": "2012-11-21T02:29:26.000Z",
  "updated": "2013-10-09T18:03:15.000Z",
  "title": "On arithmetic progressions in A + B + C",
  "authors": [
    "Kevin Henriot"
  ],
  "comment": "29 pages, fixed typos",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Our main result states that when A, B, C are subsets of Z/NZ of respective densities \\alpha,\\beta,\\gamma, the sumset A + B + C contains an arithmetic progression of length at least e^{c(\\log N)^c} for densities \\alpha > (\\log N)^{-2 + \\epsilon} and \\beta,\\gamma > e^{-c(\\log N)^c}, where c depends on \\epsilon. Previous results of this type required one set to have density at least (\\log N)^{-1 + o(1)}. Our argument relies on the method of Croot, Laba and Sisask to establish a similar estimate for the sumset A + B and on the recent advances on Roth's theorem by Sanders. We also obtain new estimates for the analogous problem in the primes studied by Cui, Li and Xue.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-09T18:03:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic progression",
      "main result states",
      "roths theorem",
      "similar estimate",
      "argument relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4917H"
    }
  }
}