{
  "id": "2007.14183",
  "version": "v1",
  "published": "2020-07-28T13:12:25.000Z",
  "updated": "2020-07-28T13:12:25.000Z",
  "title": "De Moivre polynomials of prime degree",
  "authors": [
    "Kurt Girstmair"
  ],
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "Let $p\\ge 3$ be an odd natural number. In 1738, Abraham de Moivre introduced a family of polynomials of degree $p$, all of which are solvable. So far, these polynomials were investigated only for $p=5$. We describe the factorization of these polynomials and their Galois groups for arbitrary primes $p\\ge 3$. In addition, we express all zeros of such a polynomial as rational functions of three zeros, two of which are \"conjugate\" in a certain sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-28T13:12:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F10",
      "12E10"
    ],
    "keywords": [
      "prime degree",
      "moivre polynomials",
      "odd natural number",
      "rational functions",
      "galois groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}