{
  "id": "1706.09178",
  "version": "v1",
  "published": "2017-06-28T09:12:39.000Z",
  "updated": "2017-06-28T09:12:39.000Z",
  "title": "Additive structure of totally positive quadratic integers",
  "authors": [
    "Tomáš Hejda",
    "Vítězslav Kala"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K=\\mathbb Q(\\sqrt D)$ be a real quadratic field. We obtain a presentation of the additive semigroup $\\mathcal O_K^+(+)$ of totally positive integers in $K$; its generators (indecomposable integers) and relations can be nicely described in terms of the periodic continued fraction for $\\sqrt D$. We also characterize all uniquely decomposable integers in $K$ and estimate their norms. Using these results, we prove that the semigroup $\\mathcal O_K^+(+)$ completely determines the real quadratic field $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-28T09:12:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11A55",
      "20M05"
    ],
    "keywords": [
      "totally positive quadratic integers",
      "additive structure",
      "real quadratic field",
      "periodic continued fraction",
      "presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}