{
  "id": "1404.1579",
  "version": "v1",
  "published": "2014-04-06T14:06:27.000Z",
  "updated": "2014-04-06T14:06:27.000Z",
  "title": "On the distribution of the divisor function and Hecke eigenvalues",
  "authors": [
    "Stephen Lester",
    "Nadav Yesha"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by \\'E. Fouvry, S. Ganguly, E. Kowalski, and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-06T14:06:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divisor function",
      "hecke eigenvalues",
      "short intervals",
      "arithmetic progressions",
      "complementary result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1579L"
    }
  }
}