{
  "id": "2311.12911",
  "version": "v1",
  "published": "2023-11-21T17:00:57.000Z",
  "updated": "2023-11-21T17:00:57.000Z",
  "title": "Universal quadratic forms and Dedekind zeta functions",
  "authors": [
    "Vítězslav Kala",
    "Mentzelos Melistas"
  ],
  "comment": "12 pages. Preprint",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the codifferent of $K$ is generated by a totally positive element. Motivated by a possible path to remove that assumption, we also investigate the smallest number of generators for the positive part of ideals in totally real numbers fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-21T17:00:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11E20",
      "11H06"
    ],
    "keywords": [
      "dedekind zeta functions",
      "study universal quadratic forms",
      "totally real number fields",
      "totally real numbers fields",
      "explicit upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}