{
  "id": "0902.4332",
  "version": "v3",
  "published": "2009-02-25T10:06:25.000Z",
  "updated": "2011-01-31T09:04:29.000Z",
  "title": "The distribution of the number of points modulo an integer on elliptic curves over finite fields",
  "authors": [
    "Wouter Castryck",
    "Hendrik Hubrechts"
  ],
  "comment": "21 pages; completely rewritten because of an error in the previous version",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let F be a finite field and let b and N be integers. We prove explicit estimates for the probability that the number of rational points on a randomly chosen elliptic curve E over F equals b modulo N. The underlying tool is an equidistribution result on the action of Frobenius on the N-torsion subgroup of E. Our results subsume and extend previous work by Achter and Gekeler.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-31T09:04:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52",
      "14K10"
    ],
    "keywords": [
      "finite field",
      "points modulo",
      "randomly chosen elliptic curve",
      "equidistribution result",
      "rational points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4332C"
    }
  }
}