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

作     者：Mello, Jorge 

作者机构：Oakland Univ Dept Math & Stat Rochester MI 48309 USA 

出 版 物：《EUROPEAN JOURNAL OF MATHEMATICS》 (Eur. J. Math.)

年 卷 期：2023年第9卷第4期

页      面：1-21页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The Project is funded by Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada 

主　　题：Integral points on orbits Arithmetic dynamics Quantitative estimates 

摘      要：We prove effective bounds for the set of quasi-integral points in orbits of rational maps over function fields under some conditions, generalizing previous work of Hsia and Silverman (Pacific J Math 249(2), 321-342, 2011) for orbits over function fields of characteristic zero. We then use this to prove height bounds for algebraic functions whose orbit under a rational function has multiplicative dependent elements modulo groups of S-units, generalizing recent results over number fields.