On effective ε-integrality in orbits of rational maps over function fields and multiplicative dependence

2020/12/03 by Jorge Mello, Mello, Jorge
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2012.01844

openalex publication_date 2020/12/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We give effective bounds for the set quasi-integral points in orbits of non-isotrivial rational maps over function fields under some conditions, generalizing previous work of Hsia and Silverman (2011) for orbits over function fields of characteristic zero. We then use this to prove finiteness results for algebraic functions whose orbit under a rational function has multiplicative dependent elements modulo rings of S-integers, generalizing recent results over number fields.

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