{
  "id": "1404.4648",
  "version": "v2",
  "published": "2014-04-17T20:52:27.000Z",
  "updated": "2022-11-07T22:27:22.000Z",
  "title": "Equidistribution of Elements of Norm 1 in Cyclic Extensions",
  "authors": [
    "Kathleen L. Petersen",
    "Christopher D. Sinclair"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Upon quotienting by units, the elements of norm 1 in a number field $K$ form a countable subset of a torus of dimension $r_1 + r_2 - 1$ where $r_1$ and $r_2$ are the numbers of real and pairs of complex embeddings. When $K$ is Galois with cyclic Galois group we demonstrate that this countable set is equidistributed in a finite cover of this torus with respect to a natural partial ordering induced by Hilbert's Theorem 90.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-17T20:52:27.000Z",
      "abstract": "Upon quotienting by units, the elements of norm 1 in a number field $K$ form a countable subset of a torus of dimension $r_1 + r_2 - 1$ where $r_1$ and $r_2$ are the numbers of real and pairs of complex embeddings. When $K$ is Galois with cyclic Galois group we demonstrate that this countable set is equidistributed in this torus with respect to a natural partial ordering.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2022-11-07T22:27:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K36",
      "11R42",
      "11R04",
      "11R27"
    ],
    "keywords": [
      "cyclic extensions",
      "equidistribution",
      "cyclic galois group",
      "natural partial",
      "complex embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.4648P"
    }
  }
}