Variation of Periods Modulo p in Arithmetic Dynamics

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.

15 pages

Cited by in corpus (6)

• Hilbert's irreducibility theorem and the larger sieve
• On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators
• Periods of Iterated Rational Functions over a Finite Field
• Index Divisibility in Dynamical Sequences and Cyclic Orbits Modulo $p$
• Geometry and arithmetic of verbal dynamical systems on simple groups
• Arithmetic dynamics on smooth cubic surfaces