{
  "id": "2307.07118",
  "version": "v1",
  "published": "2023-07-14T01:48:35.000Z",
  "updated": "2023-07-14T01:48:35.000Z",
  "title": "Lifting problem for universal quadratic forms over totally real cubic number fields",
  "authors": [
    "Daejun Kim",
    "Seok Hyeong Lee"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Lifting problem for universal quadratic forms asks for totally real number fields $K$ that admit a positive definite quadratic form with coefficients in $\\mathbb{Z}$ that is universal over the ring of integers of $K$. In this paper, we show that $K=\\mathbb{Q}(\\zeta_7+\\zeta_7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-14T01:48:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11R16",
      "11H06",
      "11H55"
    ],
    "keywords": [
      "totally real cubic number fields",
      "lifting problem",
      "universal quadratic forms asks",
      "real number fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}