{
  "id": "0805.1985",
  "version": "v1",
  "published": "2008-05-14T07:14:38.000Z",
  "updated": "2008-05-14T07:14:38.000Z",
  "title": "On the symmetry of arithmetical functions in almost all short intervals,IV",
  "authors": [
    "Giovanni Coppola"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the arithmetic (real) function, with f 'essentially bounded'. In particular, we obtain non-trivial bounds, through f 'correlations', for the 'Selberg integral' and the 'symmetry integral' of f in almost all short intervals $[x-h,x+h]$, $N\\le x\\le 2N$, beyond the 'classical' level, up to a very high level of distribution (for $h$ not too small). This time we go beyond Large Sieve inequality. Precisely, our method applies Weil bound for Kloosterman sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-14T07:14:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11N25"
    ],
    "keywords": [
      "short intervals",
      "arithmetical functions",
      "method applies weil bound",
      "large sieve inequality",
      "high level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1985C"
    }
  }
}