{
  "id": "0903.2866",
  "version": "v1",
  "published": "2009-03-16T22:15:32.000Z",
  "updated": "2009-03-16T22:15:32.000Z",
  "title": "Rank statistics for a family of elliptic curves over a function field",
  "authors": [
    "Carl Pomerance",
    "Igor E. Shparlinski"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter $d \\to\\infty$. This is perhaps unexpected since by a result of A. Brumer, the average rank for all elliptic curves over a function field of positive characteristic is asymptotically bounded above by 2.3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-16T22:15:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N25",
      "11R37",
      "14H52"
    ],
    "keywords": [
      "elliptic curves",
      "function field",
      "rank statistics",
      "ulmer tend",
      "average rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2866P"
    }
  }
}