Uniform Boundedness of S-Units in Arithmetic Dynamics
Number Theory
2016-01-20 v1 Dynamical Systems
Abstract
Let K be a number field and let S be a finite set of places of K which contains all the Archimedean places. For any f(z) in K(z) of degree d at least 2 which is not a d-th power in \bar{K}(z), Siegel's theorem implies that the image set f(K) contains only finitely many S-units. We conjecture that the number of such S-units is bounded by a function of |S| and d (independently of K and f). We prove this conjecture for several classes of rational functions, and show that the full conjecture follows from the Bombieri--Lang conjecture.
Keywords
Cite
@article{arxiv.1406.1990,
title = {Uniform Boundedness of S-Units in Arithmetic Dynamics},
author = {Holly Krieger and Aaron Levin and Zachary Scherr and Thomas J. Tucker and Yu Yasufuku and Michael Zieve},
journal= {arXiv preprint arXiv:1406.1990},
year = {2016}
}