{
  "id": "2303.05632",
  "version": "v2",
  "published": "2023-03-10T00:22:09.000Z",
  "updated": "2023-08-13T12:03:06.000Z",
  "title": "Dynatomic Galois groups for a family of quadratic rational maps",
  "authors": [
    "David Krumm",
    "Allan Lacy"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For every nonconstant rational function $\\phi\\in\\mathbb{Q}(x)$, the Galois groups of the dynatomic polynomials of $\\phi$ encode various properties of $\\phi$ that are of interest in the subject of arithmetic dynamics. We study here the structure of these Galois groups as $\\phi$ varies in a particular one-parameter family of maps, namely the quadratic rational maps having a critical point of period 2. In particular, we provide explicit descriptions of the third and fourth dynatomic Galois groups for maps in this family.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-08-13T12:03:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P05",
      "11S20",
      "11G30"
    ],
    "keywords": [
      "quadratic rational maps",
      "fourth dynatomic galois groups",
      "nonconstant rational function",
      "dynatomic polynomials",
      "arithmetic dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}