{
  "id": "1501.06296",
  "version": "v1",
  "published": "2015-01-26T09:36:38.000Z",
  "updated": "2015-01-26T09:36:38.000Z",
  "title": "On a conjecture of Gross and Zagier",
  "authors": [
    "Dongho Byeon",
    "Taekyung Kim",
    "Donggeon Yhee"
  ],
  "comment": "39 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Gross and Zagier conjectured that if the analytic rank of a rational elliptic curve is 1, then the order of the rational torsion subgroup of the elliptic curve divides the product of Tamagawa number, Manin constant, and the square root of the order of Tate--Shafarevich group over an imaginary quadratic field. In this paper, we show that this conjecture is true except for two explicit families of curves. We show the validity of the conjecture also for these exceptions, under another conjecture of Stein and Watkins.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-26T09:36:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05"
    ],
    "keywords": [
      "conjecture",
      "rational elliptic curve",
      "rational torsion subgroup",
      "elliptic curve divides",
      "imaginary quadratic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150106296B"
    }
  }
}