{
  "id": "2212.09461",
  "version": "v1",
  "published": "2022-12-19T13:55:14.000Z",
  "updated": "2022-12-19T13:55:14.000Z",
  "title": "Breaking the 4 barrier for the bound of a generating set of the class group",
  "authors": [
    "Loïc Grenié",
    "Giuseppe Molteni"
  ],
  "comment": "11 pages, 1 table",
  "categories": [
    "math.NT"
  ],
  "abstract": "Under the assumption of the validity of the Generalized Riemann Hypothesis, we prove that the class group of every field of degree $n$ and discriminant with absolute value $\\Delta$ can be generated using prime ideals with norm $\\leq (4-1/(2n))\\log^2\\Delta$, except for a finite number of fields of degree $n\\leq 8$. For those fields, the conclusion holds with the slightly larger limit $(4-1/(3n))\\log^2\\Delta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-19T13:55:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11R29",
      "11Y40"
    ],
    "keywords": [
      "class group",
      "generating set",
      "generalized riemann hypothesis",
      "absolute value",
      "prime ideals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}