{
  "id": "2409.07941",
  "version": "v1",
  "published": "2024-09-12T11:09:34.000Z",
  "updated": "2024-09-12T11:09:34.000Z",
  "title": "No proper generalized quadratic forms are universal over quadratic fields",
  "authors": [
    "Ondřej Chwiedziuk",
    "Matěj Doležálek",
    "Simona Hlavinková",
    "Emma Pěchoučková",
    "Zdeněk Pezlar",
    "Om Prakash",
    "Anna Růžičková",
    "Mikuláš Zindulka"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is universal. We also construct an example illustrating that the positive-definiteness condition is necessary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-12T11:09:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11E20",
      "11E25",
      "11R11",
      "11R27",
      "11R80"
    ],
    "keywords": [
      "proper generalized quadratic forms",
      "quadratic fields",
      "real quadratic number fields",
      "natural positive-definiteness condition",
      "quadratic subform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}