{
  "id": "1512.04691",
  "version": "v1",
  "published": "2015-12-15T09:35:49.000Z",
  "updated": "2015-12-15T09:35:49.000Z",
  "title": "Norms of indecomposable integers in real quadratic fields",
  "authors": [
    "Vítězslav Kala"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study totally positive, additively indecomposable integers in a real quadratic field $\\mathbb Q(\\sqrt D)$. We estimate the size of the norm of an indecomposable integer by expressing it as a power series in $u_i^{-1}$, where $\\sqrt D$ has the periodic continued fraction expansion $[u-0, \\bar{u_1, u_2, \\dots, u_{s-1}, 2u-0}]$. This enables us to find a counterexample to a conjecture of Jang-Kim [JK] concerning the maximal size of the norm of an indecomposable integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-15T09:35:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11A55"
    ],
    "keywords": [
      "real quadratic field",
      "periodic continued fraction expansion",
      "power series",
      "additively indecomposable integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151204691K"
    }
  }
}