The Michigan Mathematical Journal

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

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

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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
Received: 5 July 2017
Revised: 3 May 2018
First available in Project Euclid: 30 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1556589745

Digital Object Identifier
doi:10.1307/mmj/1556589745

Mathematical Reviews number (MathSciNet)
MR3961222

Zentralblatt MATH identifier
07084768

Subjects
Primary: 11R18: Cyclotomic extensions 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]

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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