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 generalization of the Northcott theorem replacing the finiteness of preperiodic points from a given number field by the finiteness of algebraic integers having two multiplicatively dependent elements in their orbits.
Citation
Alina Ostafe. Min Sha. Igor E. Shparlinski. Umberto Zannier. "On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem." Michigan Math. J. 68 (2) 385 - 407, June 2019. https://doi.org/10.1307/mmj/1556589745