{
  "id": "1609.02314",
  "version": "v1",
  "published": "2016-09-08T08:08:52.000Z",
  "updated": "2016-09-08T08:08:52.000Z",
  "title": "Number of Irreducible Polynomials over Finite Fields with First Two Coefficients Fixed",
  "authors": [
    "Gary McGuire",
    "Emrah Sercan Yılmaz"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1605.07229",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $p$ be an odd prime number. For any positive integers $n\\geq 2, r\\geq 1$ we present formulae for the number of irreducible polynomials of degree $n$ over the finite field $\\mathbb F_{p^r}$ where the coefficients of $x^{n-1}$ and $x^{n-2}$ are fixed. Our proof involves counting the number of points on an algebraic curve over finite fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-08T08:08:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "irreducible polynomials",
      "coefficients",
      "odd prime number",
      "algebraic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}