{
  "id": "2011.02968",
  "version": "v1",
  "published": "2020-11-05T16:50:06.000Z",
  "updated": "2020-11-05T16:50:06.000Z",
  "title": "Effective finiteness of solutions to certain differential and difference equations",
  "authors": [
    "Patrick Ingram"
  ],
  "categories": [
    "math.NT",
    "math.CV"
  ],
  "abstract": "For R(z, w) rational with complex coefficients, of degree at least 2 in w, we show that the number of rational functions f(z) solving the difference equation f(z+1)=R(z, f(z)) is finite and bounded just in terms of the degrees of R in the two variables. This complements a result of Yanagihara, who showed that any finite-order meromorphic solution to this sort of difference equation must be a rational function. We prove a similar result for the differential equation f'(z)=R(z, f(z)), building on a result of Eremenko.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-05T16:50:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "difference equation",
      "effective finiteness",
      "rational function",
      "finite-order meromorphic solution",
      "complex coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}