{
  "id": "1705.03671",
  "version": "v1",
  "published": "2017-05-10T09:34:42.000Z",
  "updated": "2017-05-10T09:34:42.000Z",
  "title": "Arity of universal quadratic forms over real quadratic fields",
  "authors": [
    "Valentin Blomer",
    "Vítězslav Kala"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field $\\mathbb Q(\\sqrt D)$ and obtain lower and upper bounds for it in terms of certain sums of coefficients of the associated continued fraction. We also estimate such sums in terms of $D$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T09:34:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11R11",
      "11A55"
    ],
    "keywords": [
      "real quadratic field",
      "definite diagonal universal quadratic form",
      "positive definite diagonal universal quadratic",
      "totally positive definite diagonal universal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}