{
  "id": "math/0003244",
  "version": "v1",
  "published": "2000-03-27T00:00:00.000Z",
  "updated": "2000-03-27T00:00:00.000Z",
  "title": "Imaginary quadratic fields k with Cl_2(k) = (2,2^m) and Rank Cl_2(k^1) = 2",
  "authors": [
    "Elliot Benjamin",
    "Franz Lemmermeyer",
    "Chip Snyder"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We classify all complex quadratic number fields with 2-class group of type (2,2^m) whose Hilbert 2-class fields have class groups of 2-rank equal to 2. These fields all have 2-class field tower of length 2. We still don't know examples of fields with 2-class field tower of length 3, but the smallest candidate is the field with discriminant -1015.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-27T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic fields",
      "field tower",
      "complex quadratic number fields",
      "class groups",
      "smallest candidate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......3244B"
    }
  }
}