{
  "id": "2212.09734",
  "version": "v1",
  "published": "2022-12-19T18:54:57.000Z",
  "updated": "2022-12-19T18:54:57.000Z",
  "title": "Characterization of norm forms via their values at integer points",
  "authors": [
    "George Tomanov"
  ],
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "We obtain a characterization of the algebraic and quasi-algebraic norm forms in terms of their values at integer points. As a consequence, we get a bijective correspondence between this kind of forms and the compact orbits for the action of the maximal tori of any rank on the space of unimodular lattices in $\\R^n$. The result is relevant to a conjecture of Cassels and Swinnerton-Dyer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-19T18:54:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer points",
      "characterization",
      "quasi-algebraic norm forms",
      "compact orbits",
      "maximal tori"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}