Primitive prime divisors in the critical orbit of z^d+c

Details Primitive prime divisors in the critical orbit of z^d+c Primitive prime divisors in the critical orbit of z^d+c

2012-03-12

arxiv.org/abs/1203.2555v1

Mathematics

Dynamical Systems

30 pages

Scientific paper

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.

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