{
  "id": "1104.5031",
  "version": "v1",
  "published": "2011-04-26T20:44:37.000Z",
  "updated": "2011-04-26T20:44:37.000Z",
  "title": "Surjectivity of mod 2^n representations of elliptic curves",
  "authors": [
    "Tim Dokchitser",
    "Vladimir Dokchitser"
  ],
  "comment": "3 pages",
  "journal": "Math. Zeitschrift, Vol. 272, Issue 3-4 (2012), 961-964",
  "doi": "10.1007/s00209-011-0967-7",
  "categories": [
    "math.NT"
  ],
  "abstract": "For an elliptic curve E over Q, the Galois action on the l-power torsion points defines representations whose images are subgroups of GL_2(Z/l^n Z). There are three exceptional prime powers l^n=2,3,4 when surjectivity of the mod l^n representation does not imply that for l^(n+1). Elliptic curves with surjective mod 3 but not mod 9 representation have been classified by Elkies. The purpose of this note is to do this in the other two cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-26T20:44:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11F80"
    ],
    "keywords": [
      "elliptic curve",
      "surjectivity",
      "l-power torsion points defines representations",
      "exceptional prime powers",
      "galois action"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.5031D"
    }
  }
}