{
  "id": "1307.7691",
  "version": "v3",
  "published": "2013-07-29T19:24:31.000Z",
  "updated": "2014-03-20T07:28:38.000Z",
  "title": "On the class numbers of the fields of the p^n-torsion points of certain elliptic curves over Q",
  "authors": [
    "Fumio Sairaiji",
    "Takuya Yamauchi"
  ],
  "comment": "11 pages, the all conditions in main theorem are removed",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let E be an elliptic curve over Q with prime conductor p. For each non-negative integer n we put K_n:=Q(E[p^n]). The aim of this paper is to estimate the order of the p-Sylow group of the ideal class group of K_n. We give a lower bounds in terms of the Mordell-Weil rank of $E(\\Q)$. As an application of our result, we give an example such that p^{2n} divides the class number of the field $K_n$ in the case of $p=5077$ for each positive integer n.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-20T07:28:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic curve",
      "class number",
      "ideal class group",
      "mordell-weil rank",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7691S"
    }
  }
}