{
  "id": "1210.1562",
  "version": "v2",
  "published": "2012-10-04T19:53:43.000Z",
  "updated": "2012-10-15T18:17:13.000Z",
  "title": "On irreducible polynomials over finite fields",
  "authors": [
    "Zhi-Wei Sun"
  ],
  "comment": "7 pages. Add a result on N_{n+1}(q)/N_n(q) and its proof",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "For n=1,2,3,... let N_n(q) denote the number of monic irreducible polynomials over the finite field F_q. We mainly show that the sequence N_n(q)^{1/n} (n>e^{3+7/(q-1)^2}) is strictly increasing and the sequence N_{n+1}(q)^{1/(n+1)}/N_n(q)^{1/n} (n>=5.835*10^{14}) is strictly decreasing. We also prove that if q>8 then N_{n+1}(q)/N_n(q) (n=1,2,3,...) is strictly increasing.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-15T18:17:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12E20",
      "05A10",
      "11B99",
      "11C99"
    ],
    "keywords": [
      "finite field",
      "monic irreducible polynomials",
      "strictly increasing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1562S"
    }
  }
}