{
  "id": "1810.03142",
  "version": "v1",
  "published": "2018-10-07T13:34:54.000Z",
  "updated": "2018-10-07T13:34:54.000Z",
  "title": "A note on the stability of trinomials over finite fields",
  "authors": [
    "Omran Ahmadi",
    "Kosrov Monsef-Shokri"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "A polynomial $f(x)$ over a field $K$ is called stable if all of its iterates are irreducible over $K$. In this paper we study the stability of trinomials over finite fields. Specially, we show that if $f(x)$ is a trinomial of even degree over the binary field $\\mathbb{F}_2$, then $f(x)$ is not stable. We prove a similar result for some families of monic trinomials over finite fields of odd characteristic. These results are obtained towards the resolution of a conjecture on the instability of polynomials over finite fields whose degrees are divisible by the characteristic of the underlying field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-07T13:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "12E20"
    ],
    "keywords": [
      "finite fields",
      "odd characteristic",
      "monic trinomials",
      "polynomial",
      "binary field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}