{
  "id": "math/0512260",
  "version": "v1",
  "published": "2005-12-13T10:46:07.000Z",
  "updated": "2005-12-13T10:46:07.000Z",
  "title": "Asymptotics of number fields and the Cohen--Lenstra heuristics",
  "authors": [
    "Jürgen Klüners"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the asymptotics conjecture of Malle for dihedral groups $D_\\ell$ of order $2\\ell$, where $\\ell$ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-13T10:46:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R45",
      "11R29",
      "11R32",
      "12F12"
    ],
    "keywords": [
      "cohen-lenstra heuristics",
      "class groups",
      "quadratic number fields",
      "expected upper bounds",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12260K"
    }
  }
}