{
  "id": "0810.0485",
  "version": "v1",
  "published": "2008-10-02T17:08:02.000Z",
  "updated": "2008-10-02T17:08:02.000Z",
  "title": "Exact solutions to Waring's problem for finite fields",
  "authors": [
    "Arne Winterhof",
    "Christiaan van de Woestijne"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The Waring function $g(k,q)$ measures the difficulty of Waring's problem for $k$th powers in the field of $q$ elements. Its calculation seems to be difficult, and many partial results have been published, notably upper bounds for certain regions of the $k$-$q$-plane. In this paper, we compute the exact value of $g(k,q)$ for two infinite families of exponent-field pairs. In these, $k$ is large compared to $q$. We use a new method of proof that is mainly combinatorial in nature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-02T17:08:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P05",
      "11T41",
      "90C10",
      "94B65"
    ],
    "keywords": [
      "warings problem",
      "exact solutions",
      "finite fields",
      "th powers",
      "partial results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0485W"
    }
  }
}