{
  "id": "1304.5829",
  "version": "v1",
  "published": "2013-04-22T04:07:30.000Z",
  "updated": "2013-04-22T04:07:30.000Z",
  "title": "Class numbers of ternary quadratic forms",
  "authors": [
    "Wai Kiu Chan",
    "Byeong-Kweon Oh"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "G.L. Watson \\cite{watson1, watson2} introduced a set of transformations, called Watson transformations by most recent authors, in his study of the arithmetic of integral quadratic forms. These transformations change an integral quadratic form to another integral quadratic form with a smaller discriminants, but preserve many arithmetic properties at the same time. In this paper, we study the change of class numbers of positive definite ternary integral quadratic formula along a sequence of Watson transformations, thus providing a new and effective way to compute the class number of positive definite ternary integral quadratic forms. Explicit class number formulae for many genera of positive definite ternary integral quadratic forms are derived as illustrations of our method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-22T04:07:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11E20",
      "11E41"
    ],
    "keywords": [
      "class number",
      "positive definite ternary integral quadratic",
      "ternary quadratic forms",
      "definite ternary integral quadratic forms",
      "ternary integral quadratic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.5829K"
    }
  }
}