{
  "id": "2103.07955",
  "version": "v1",
  "published": "2021-03-14T15:43:28.000Z",
  "updated": "2021-03-14T15:43:28.000Z",
  "title": "A new family of exceptional rational functions",
  "authors": [
    "Zhiguo Ding",
    "Michael E. Zieve"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For each odd prime power q, we construct an infinite sequence of rational functions f(X) in F_q(X), each of which is exceptional, which means that for infinitely many n the map c-->f(c) induces a bijection of P^1(F_{q^n}). Moreover, each of our functions f(X) is indecomposable, which means that it cannot be written as the composition of lower-degree rational functions in F_q(X). In case q is not a power of 3, these are the first known examples of indecomposable exceptional rational functions f(X) over F_q which have non-solvable monodromy groups and have arbitrarily large degree. These are also the first known examples of wildly ramified indecomposable exceptional rational functions f(X), other than linear changes of polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-14T15:43:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11R32"
    ],
    "keywords": [
      "odd prime power",
      "lower-degree rational functions",
      "ramified indecomposable exceptional rational functions",
      "infinite sequence",
      "wildly ramified indecomposable exceptional rational"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}