{
  "id": "1906.03730",
  "version": "v1",
  "published": "2019-06-09T22:44:47.000Z",
  "updated": "2019-06-09T22:44:47.000Z",
  "title": "Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions",
  "authors": [
    "André Macedo",
    "Rachel Newton"
  ],
  "comment": "40 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K/k$ be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for $K/k$ and the defect of weak approximation for the norm one torus $R^1_{K/k} \\mathbb{G}_m$. We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of $K/k$ has symmetric or alternating Galois group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-09T22:44:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11E72",
      "11R37",
      "20G30"
    ],
    "keywords": [
      "hasse norm principle",
      "explicit methods",
      "applications",
      "weak approximation",
      "number fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}