{
  "id": "2301.10136",
  "version": "v1",
  "published": "2023-01-24T17:07:59.000Z",
  "updated": "2023-01-24T17:07:59.000Z",
  "title": "A note on the Hasse norm principle",
  "authors": [
    "Peter Koymans",
    "Nick Rome"
  ],
  "comment": "8 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be a finite, abelian group. We show that the density of $A$-extensions satisfying the Hasse norm principle exists, when the extensions are ordered by discriminant. This strengthens earlier work of Frei--Loughran--Newton \\cite{FLN}, who obtained a density result under the additional assumption that $A/A[\\ell]$ is cyclic with $\\ell$ denoting the smallest prime divisor of $\\# A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-24T17:07:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R45",
      "14G12"
    ],
    "keywords": [
      "hasse norm principle",
      "smallest prime divisor",
      "strengthens earlier work",
      "density result",
      "abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}