{
  "id": "1103.3635",
  "version": "v1",
  "published": "2011-03-18T14:42:40.000Z",
  "updated": "2011-03-18T14:42:40.000Z",
  "title": "On a conjecture of polynomials with prescribed range",
  "authors": [
    "Muratović-Ribić",
    "Qiang Wang"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We show that, for any integer $\\ell$ with $q-\\sqrt{p} -1 \\leq \\ell < q-3$ where $q=p^n$ and $p>9$, there exists a multiset $M$ satisfying that $0\\in M$ has the highest multiplicity $\\ell$ and $\\sum_{b\\in M} b =0$ such that every polynomial over finite fields $\\fq$ with the prescribed range $M$ has degree greater than $\\ell$. This implies that Conjecture 5.1. in \\cite{gac} is false over finite field $\\fq$ for $p > 9$ and $k:=q-\\ell -1 \\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-18T14:42:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prescribed range",
      "polynomial",
      "conjecture",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.3635M"
    }
  }
}