{
  "id": "1010.5341",
  "version": "v1",
  "published": "2010-10-26T09:35:32.000Z",
  "updated": "2010-10-26T09:35:32.000Z",
  "title": "On the distribution of Galois groups",
  "authors": [
    "Rainer Dietmann"
  ],
  "comment": "6 pages",
  "doi": "10.1112/S0025579311002105",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $G$ be a subgroup of the symmetric group $S_n$, and let $\\delta_G=|S_n/G|^{-1}$ where $|S_n/G|$ is the index of $G$ in $S_n$. Then there are at most $O_{n, \\epsilon}(H^{n-1+\\delta_G+\\epsilon})$ monic integer polynomials of degree $n$ having Galois group $G$ and height not exceeding $H$, so there are only `few' polynomials having `small' Galois group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-26T09:35:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C08",
      "11R32",
      "11G35"
    ],
    "keywords": [
      "galois group",
      "distribution",
      "monic integer polynomials",
      "symmetric group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5341D"
    }
  }
}