{
  "id": "1001.3356",
  "version": "v1",
  "published": "2010-01-19T16:28:13.000Z",
  "updated": "2010-01-19T16:28:13.000Z",
  "title": "Equivalence of polynomial conjectures in additive combinatorics",
  "authors": [
    "Shachar Lovett"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We study two conjectures in additive combinatorics. The first is the polynomial Freiman-Ruzsa conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for $U^3$, which relates to functions which locally look like quadratics. In both cases a weak form, with exponential decay of parameters is known, and a strong form with only a polynomial loss of parameters is conjectured. Our main result is that the two conjectures are in fact equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-19T16:28:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B10",
      "11B13"
    ],
    "keywords": [
      "additive combinatorics",
      "polynomial conjectures",
      "equivalence",
      "polynomial freiman-ruzsa conjecture",
      "inverse gowers conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.3356L"
    }
  }
}