{
  "id": "1011.4501",
  "version": "v2",
  "published": "2010-11-19T19:14:39.000Z",
  "updated": "2011-04-14T05:24:48.000Z",
  "title": "Norm-Euclidean Galois fields",
  "authors": [
    "Kevin J. McGown"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let K be a Galois number field of prime degree $\\ell$. Heilbronn showed that for a given $\\ell$ there are only finitely many such fields that are norm-Euclidean. In the case of $\\ell=2$ all such norm-Euclidean fields have been identified, but for $\\ell\\neq 2$, little else is known. We give the first upper bounds on the discriminants of such fields when $\\ell>2$. Our methods lead to a simple algorithm which allows one to generate a list of candidate norm-Euclidean fields up to a given discriminant, and we provide some computational results.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-14T05:24:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11R04",
      "11Y40"
    ],
    "keywords": [
      "norm-euclidean galois fields",
      "galois number field",
      "candidate norm-euclidean fields",
      "first upper bounds",
      "discriminant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4501M"
    }
  }
}