On multiplicative dependence of values of rational functions

Alina Ostafe, Min Sha, Igor E. Shparlinski, Umberto Zannier

Published 2017-06-19Version 1

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.