On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem

2017/06/19 by Alina Ostafe, Min Sha, Ostafe, Alina +5
Mathematics · #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1706.05874

openalex publication_date 2017/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Related

• Multiplicative dependence among iterated values of rational functions modulo finitely generated groups
• On multiplicative dependence between elements of polynomial orbits
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