{
  "id": "2402.17994",
  "version": "v2",
  "published": "2024-02-28T02:18:59.000Z",
  "updated": "2024-04-10T12:14:30.000Z",
  "title": "Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm",
  "authors": [
    "James Leng",
    "Ashwin Sah",
    "Mehtaab Sawhney"
  ],
  "comment": "100 pages",
  "categories": [
    "math.CO",
    "math.DS",
    "math.NT"
  ],
  "abstract": "We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input recent work of the first author regarding the equidistribution of nilsequences. In a companion paper, this result will be used to improve the bounds on Szemer\\'{e}di's theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-10T12:14:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse theorem",
      "quasipolynomial bounds",
      "crucial input",
      "companion paper",
      "first author regarding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 100,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}