Perfect powers in value sets and orbits of polynomials
Number Theory
2021-09-24 v3
Abstract
We show the finiteness of perfect powers in orbits of polynomial dynamical systems over an algebraic number field. We also obtain similar results for perfect powers represented by ratios of consecutive elements in orbits. Assuming the -Conjecture for number fields, we obtain a finiteness result for powers in ratios of arbitrary elements in orbits.
Cite
@article{arxiv.1907.12057,
title = {Perfect powers in value sets and orbits of polynomials},
author = {Alina Ostafe and Lukas Pottmeyer and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1907.12057},
year = {2021}
}
Comments
In this version we fixed a few inaccuracies, and heavily simplified the proof of Theorem 1.2. This version is accepted for publication in the New York Journal of Mathematics