Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers

2020/01/27 by Ray Li, Li, Ray, Igor E. Shparlinski +1
Computer Science · Mathematics · #11R27 #37P05 (Primary) #37P15 (Secondary) #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.2001.09721

openalex publication_date 2020/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain effective bounds on the heights of algebraic integers whose orbits contain multiplicatively dependent values modulo S-integers. Our method is based on a new upper bound on the so-called S-height of polynomial values over the ring of integers of \mathbbK. Our results provide an effective variant of a recent result of A.Bérczes, A.Ostafe, I.E.Shparlinski and J.H.Silverman (arXiv:1811.04971) on multiplicative dependence modulo a finitely generated subgroup by eliminating the use of non-effective results by K.F.Roth and G.Faltings.

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