{
  "id": "1808.02148",
  "version": "v1",
  "published": "2018-08-06T23:02:04.000Z",
  "updated": "2018-08-06T23:02:04.000Z",
  "title": "$\\ell$-torsion in class groups of certain families of $D_4$-quartic fields",
  "authors": [
    "Chen An"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an upper bound for $\\ell$-torsion in class groups of almost all fields in certain families of $D_4$-quartic fields. Our key tools are a new Chebotarev density theorem for these families of $D_4$-quartic fields and a lower bound for the number of fields in the families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-06T23:02:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quartic fields",
      "class groups",
      "chebotarev density theorem",
      "upper bound",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}