{
  "id": "0709.3648",
  "version": "v3",
  "published": "2007-09-23T16:54:09.000Z",
  "updated": "2007-12-31T23:50:57.000Z",
  "title": "On the Correlations, Selberg Integral and Symmetry of Sieve Functions in Short Intervals",
  "authors": [
    "Giovanni Coppola"
  ],
  "comment": "Plain TeX; typos added",
  "journal": "J. Comb. Number Theory 2(2) (2010), 91-105",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the arithmetic (real) function f=g*1, with g \"essentially bounded\" and supported over the integers of [1,Q]. 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<x<2N, beyond the \"classical\" level, up to level of distribution, say, lambda=log Q/log N < 2/3 (for enough large h). This time we don't apply Large Sieve inequality, as in our paper [C-S]. Precisely, our method is completely elementary.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-12-31T23:50:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11N25"
    ],
    "keywords": [
      "short intervals",
      "selberg integral",
      "sieve functions",
      "correlations",
      "dont apply large sieve inequality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.3648C"
    }
  }
}