{
  "id": "1309.0443",
  "version": "v1",
  "published": "2013-09-02T15:42:47.000Z",
  "updated": "2013-09-02T15:42:47.000Z",
  "title": "The asymptotic formula in Waring's problem: higher order expansions",
  "authors": [
    "Robert C. Vaughan",
    "Trevor D. Wooley"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-02T15:42:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P05",
      "11P55"
    ],
    "keywords": [
      "higher order expansions",
      "warings problem",
      "asymptotic formula",
      "explicit multi-term asymptotic expansion",
      "positive integral k-th powers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0443V"
    }
  }
}