{
  "id": "2002.00500",
  "version": "v1",
  "published": "2020-02-02T22:20:55.000Z",
  "updated": "2020-02-02T22:20:55.000Z",
  "title": "Exceptional scatteredness in prime degree",
  "authors": [
    "Andrea Ferraguti",
    "Giacomo Micheli"
  ],
  "categories": [
    "math.NT",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "Let $q$ be an odd prime power and $n$ be a positive integer. Let $\\ell\\in \\mathbb F_{q^n}[x]$ be a $q$-linearised $t$-scattered polynomial of linearized degree $r$. Let $d=\\max\\{t,r\\}$ be an odd prime number. In this paper we show that under these assumptions it follows that $\\ell=x$. Our technique involves a Galois theoretical characterization of $t$-scattered polynomials combined with the classification of transitive subgroups of the general linear group over the finite field $\\mathbb F_q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-02T22:20:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11T71",
      "11R45"
    ],
    "keywords": [
      "prime degree",
      "exceptional scatteredness",
      "odd prime power",
      "general linear group",
      "scattered polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}