{
  "id": "0911.3040",
  "version": "v1",
  "published": "2009-11-16T14:25:42.000Z",
  "updated": "2009-11-16T14:25:42.000Z",
  "title": "On two-dimensional continued fractions for the integer hyperbolic matrices with small norm",
  "authors": [
    "Oleg Karpenkov"
  ],
  "journal": "Uspekhi Mat. Nauk 59 (2004), no. 5(359), 149--150; translation in Russian Math. Surveys 59 (2004), no. 5, 959--960",
  "doi": "10.1070/RM2004v059n05ABEH000778",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this note we classify two-dimensional continued fractions for cubic irrationalities constructed by matrices with not large norm ($|*| \\le 6$). The classification is based on the following new result: the class of matrices with an irreducible characteristic polynomial over the field of rational numbers is the class of matrices of frobenius type iff there exists an integer solution for a certain equation with integer coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-16T14:25:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11H06",
      "52C07"
    ],
    "keywords": [
      "integer hyperbolic matrices",
      "small norm",
      "cubic irrationalities",
      "integer coefficients",
      "large norm"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.3040K"
    }
  }
}