{
  "id": "2112.04208",
  "version": "v1",
  "published": "2021-12-08T10:14:39.000Z",
  "updated": "2021-12-08T10:14:39.000Z",
  "title": "An elementary proof of Takagi's theorem on the differential composition of polynomials",
  "authors": [
    "Alan D. Sokal"
  ],
  "comment": "LaTeX2e, 4 pages. Accepted for publication in the American Mathematical Monthly",
  "journal": "Amer. Math. Monthly 129, 381--384 (2022)",
  "doi": "10.1080/00029890.2022.2027719",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "I give a short and completely elementary proof of Takagi's 1921 theorem on the zeros of a composite polynomial $f(d/dz) \\, g(z)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-12-08T10:14:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C15",
      "30C10"
    ],
    "keywords": [
      "elementary proof",
      "differential composition",
      "takagis theorem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}