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June 2019 On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem
Alina Ostafe, Min Sha, Igor E. Shparlinski, Umberto Zannier
Michigan Math. J. 68(2): 385-407 (June 2019). DOI: 10.1307/mmj/1556589745

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

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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

Information

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

zbMATH: 07084768
MathSciNet: MR3961222
Digital Object Identifier: 10.1307/mmj/1556589745

Subjects:
Primary: 11R18, 37F10

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 2 • June 2019
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