{
  "id": "0801.2577",
  "version": "v2",
  "published": "2008-01-16T21:38:49.000Z",
  "updated": "2008-04-01T17:42:52.000Z",
  "title": "A new proof of Roth's theorem on arithmetic progressions",
  "authors": [
    "Ernie Croot",
    "Olof Sisask"
  ],
  "comment": "6 pages. To appear in Proceedings of the AMS",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We present a proof of Roth's theorem that follows a slightly different structure to the usual proofs, in that there is not much iteration. Although our proof works using a type of density increment argument (which is typical of most proofs of Roth's theorem), we do not pass to a progression related to the large Fourier coefficients of our set (as most other proofs of Roth do). Furthermore, in our proof, the density increment is achieved through an application of a quantitative version of Varnavides's theorem, which is perhaps unexpected.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-01T17:42:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D99"
    ],
    "keywords": [
      "roths theorem",
      "arithmetic progressions",
      "large fourier coefficients",
      "density increment argument",
      "usual proofs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.2577C"
    }
  }
}