{
  "id": "math/0403225",
  "version": "v3",
  "published": "2004-03-14T07:53:27.000Z",
  "updated": "2004-07-16T08:07:15.000Z",
  "title": "Elliptic curves and continued fractions",
  "authors": [
    "Alfred J. van der Poorten"
  ],
  "comment": "v1; final -- I hope",
  "categories": [
    "math.NT"
  ],
  "abstract": "We detail the continued fraction expansion of the square root of the general monic quartic polynomial, noting that each line of the expansion corresponds to addition of the divisor at infinity. We analyse the data yielded by the general expansion. In that way we obtain `elliptic sequences' satisfying Somos relations. I mention several new results on such sequences. The paper includes a detailed `reminder exposition' on continued fractions of quadratic irrationals in function fields.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-07-16T08:07:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A55",
      "11G05",
      "14H05",
      "14H52"
    ],
    "keywords": [
      "elliptic curves",
      "general monic quartic polynomial",
      "function fields",
      "continued fraction expansion",
      "square root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3225V"
    }
  }
}