Primitive prime divisors in the critical orbit of z^d+c
Dynamical Systems
2012-09-03 v2 Number Theory
Abstract
We prove the finiteness of the Zsigmondy set associated to the critical orbit of f(z) = z^d+c for rational values of c by finding an effective bound on the size of the set. For non-recurrent critical orbits, the Zsigmondy set is explicitly computed by utilizing effective dynamical height bounds. In the general case, we use Thue-style Diophantine approximation methods to bound the size of the Zsigmondy set when d >2, and complex-analytic methods when d=2.
Keywords
Cite
@article{arxiv.1203.2555,
title = {Primitive prime divisors in the critical orbit of z^d+c},
author = {Holly Krieger},
journal= {arXiv preprint arXiv:1203.2555},
year = {2012}
}
Comments
This version includes numerous typographical changes and expanded exposition, and a simplified proof of Theorem 6.1. 30 pages, to appear in International Math Research Notices