{
  "id": "1706.05874",
  "version": "v1",
  "published": "2017-06-19T10:50:24.000Z",
  "updated": "2017-06-19T10:50:24.000Z",
  "title": "On multiplicative dependence of values of rational functions",
  "authors": [
    "Alina Ostafe",
    "Min Sha",
    "Igor E. Shparlinski",
    "Umberto Zannier"
  ],
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dependence in the orbits of a univariate polynomial dynamical system. We also obtain a broad generalisation of the Northcott theorem replacing the finiteness of preperiodic points from a given number field by the finiteness of initial points with two multiplicatively dependent elements in their orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-19T10:50:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational functions",
      "number field",
      "univariate polynomial dynamical system",
      "study multiplicative dependence",
      "initial points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}