{
  "id": "1611.07088",
  "version": "v1",
  "published": "2016-11-21T22:46:25.000Z",
  "updated": "2016-11-21T22:46:25.000Z",
  "title": "Statistics of genus numbers of cubic fields",
  "authors": [
    "Kevin J. McGown",
    "Amanda Tucker"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that approximately $96.23\\%$ of cubic fields when ordered by discriminant have genus number one. We compute in general the exact proportion of cubic fields with a given genus number, as well as the average genus number. Finally, we show that a positive proportion of totally real cubic fields with genus number one fail to be norm-Euclidean.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-21T22:46:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R16",
      "11R45",
      "11R29",
      "11A05"
    ],
    "keywords": [
      "statistics",
      "totally real cubic fields",
      "average genus number",
      "exact proportion",
      "positive proportion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}