{
  "id": "1811.00718",
  "version": "v1",
  "published": "2018-11-02T03:00:45.000Z",
  "updated": "2018-11-02T03:00:45.000Z",
  "title": "Quantitative bounds in the inverse theorem for the Gowers $U^{s+1}$-norms over cyclic groups",
  "authors": [
    "Frederick Manners"
  ],
  "comment": "123 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We provide a new proof of the inverse theorem for the Gowers $U^{s+1}$-norm over groups $H=\\mathbb Z/N\\mathbb Z$ for $N$ prime. This proof gives reasonable quantitative bounds (the worst parameters are double-exponential), and in particular does not make use of regularity or non-standard analysis, both of which are new for $s \\ge 3$ in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-02T03:00:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse theorem",
      "cyclic groups",
      "worst parameters",
      "non-standard analysis",
      "double-exponential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 123,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}