{
  "id": "1701.04615",
  "version": "v1",
  "published": "2017-01-17T10:52:15.000Z",
  "updated": "2017-01-17T10:52:15.000Z",
  "title": "Continued fraction algorithms and Lagrange's theorem in ${\\mathbb Q}_p$",
  "authors": [
    "Asaki Saito",
    "Jun-ichi Tamura",
    "Shin-ichi Yasutomi"
  ],
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of ${\\mathbb Q}_p$ over ${\\mathbb Q}$ and gives a finite expansion for every rational number. We also give, for each of our algorithms, the complete characterization of elements having purely periodic expansions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-17T10:52:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continued fraction algorithms",
      "lagranges theorem",
      "purely periodic expansions",
      "complete characterization",
      "eventually periodic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}