{
  "id": "1302.1454",
  "version": "v1",
  "published": "2013-02-06T17:51:53.000Z",
  "updated": "2013-02-06T17:51:53.000Z",
  "title": "On Linnik's conjecture: sums of squares and microsquares",
  "authors": [
    "Trevor D. Wooley"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that almost all natural numbers n not divisible by 4, and not congruent to 7 modulo 8, are represented as the sum of three squares, one of which is the square of an integer no larger than (log n)^{1+e} (any e>0). This answers a conjecture of Linnik for almost all natural numbers, and sharpens a conclusion of Bourgain, Rudnick and Sarnak concerning nearest neighbour distances between normalised integral points on the sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-06T17:51:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E25",
      "11D85",
      "11P55"
    ],
    "keywords": [
      "linniks conjecture",
      "natural numbers",
      "microsquares",
      "sarnak concerning nearest neighbour distances",
      "normalised integral points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1454W"
    }
  }
}