Variation of Periods Modulo p in Arithmetic Dynamics
Number Theory
2011-05-30 v1 Dynamical Systems
Abstract
Let F : V --> V be a self-morphism of a quasiprojective variety defined over a number field K and let P be a point in V(K) with infinite orbit under iteration of F. For each prime ideal p of good reduction, let m_p(F,P) be the size of the F-orbit of the reduction of P modulo p. Fix any e > 0. We show that for almost all primes p, in the sense of analytic density, the orbit size m_p(F,P) is larger than (log(N(p)))^(1-e), where N(p) is the norm of the ideal p.
Cite
@article{arxiv.0707.1505,
title = {Variation of Periods Modulo p in Arithmetic Dynamics},
author = {Joseph H. Silverman},
journal= {arXiv preprint arXiv:0707.1505},
year = {2011}
}
Comments
15 pages