{
  "id": "math/0412135",
  "version": "v2",
  "published": "2004-12-07T12:23:16.000Z",
  "updated": "2005-02-21T12:54:01.000Z",
  "title": "Poisson statistics via the Chinese remainder theorem",
  "authors": [
    "A. Granville",
    "P. Kurlberg"
  ],
  "comment": "32 pages. Lemma 15 corrected (for the case k=2.) Added reference",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the Chinese remainder theorem. We give a sufficient criterion for the spacing distribution to be Poissonian as the number of prime factors of q tends to infinity, and as an application we show that the value set of a generic polynomial modulo q have Poisson spacings. We also study the spacings of subsets of Z/q_1q_2Z that are created via the Chinese remainder theorem from subsets of Z/q_1Z and Z/q_2Z (for q_1,q_2 coprime), and give criteria for when the spacings modulo q_1q_2 are Poisson. We also give some examples when the spacings modulo q_1q_2 are not Poisson, even though the spacings modulo q_1 and modulo q_2 are both Poisson.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-21T12:54:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N69",
      "11K36",
      "11K06"
    ],
    "keywords": [
      "chinese remainder theorem",
      "poisson statistics",
      "spacings modulo",
      "generic polynomial modulo",
      "prime factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12135G"
    }
  }
}