## The Michigan Mathematical Journal

### On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem

#### 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.

#### Article information

Source
Michigan Math. J., Volume 68, Issue 2 (2019), 385-407.

Dates
Revised: 3 May 2018
First available in Project Euclid: 30 April 2019

https://projecteuclid.org/euclid.mmj/1556589745

Digital Object Identifier
doi:10.1307/mmj/1556589745

Mathematical Reviews number (MathSciNet)
MR3961222

Zentralblatt MATH identifier
07084768

#### Citation

Ostafe, Alina; Sha, Min; Shparlinski, Igor E.; Zannier, Umberto. On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem. Michigan Math. J. 68 (2019), no. 2, 385--407. doi:10.1307/mmj/1556589745. https://projecteuclid.org/euclid.mmj/1556589745

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