{
  "id": "1009.3998",
  "version": "v3",
  "published": "2010-09-21T05:41:11.000Z",
  "updated": "2011-03-27T09:40:56.000Z",
  "title": "An inverse theorem for the Gowers U^{s+1}[N]-norm",
  "authors": [
    "Ben Green",
    "Terence Tao",
    "Tamar Ziegler"
  ],
  "comment": "116 pages. Submitted",
  "categories": [
    "math.CO",
    "math.DS"
  ],
  "abstract": "We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we establish that if f : [N] -> [-1,1] is a function with || f ||_{U^{s+1}[N]} > \\delta then there is a bounded-complexity s-step nilsequence F(g(n)\\Gamma) which correlates with f, where the bounds on the complexity and correlation depend only on s and \\delta. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-27T09:40:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B30"
    ],
    "keywords": [
      "inverse theorem",
      "hardy-littlewood prime tuples conjecture",
      "bounded-complexity s-step nilsequence",
      "finite complexity",
      "linear system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 116,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3998G"
    }
  }
}