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On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem (1706.05874v5)
Published 19 Jun 2017 in math.NT and 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.
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