Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers
Number Theory
2020-01-28 v1 Dynamical Systems
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 . Our results provide an effective variant of a recent result of A.B\'erczes, 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.
Cite
@article{arxiv.2001.09721,
title = {Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers},
author = {Ray Li and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:2001.09721},
year = {2020}
}