New York Journal of Mathematics
Volume 14 (2008) 601-616


Joseph H. Silverman

Variation of periods modulo p in arithmetic dynamics

Published: October 26, 2008
Keywords: Arithmetic dynamical systems, orbit modulo p
Subject: Primary: 11G35; Secondary: 11B37, 14G40, 37F10

Let ϕ:V→ V be a self-morphism of a quasiprojective variety defined over a number field K and let P∈ V(K) be a point with infinite orbit under iteration of ϕ. For each prime p of good reduction, let mp(ϕ,P) be the size of the ϕ-orbit of the reduction of P modulo p. Fix any ε>0. We show that for almost all primes p in the sense of analytic density, the orbit size mp(ϕ,P) is larger than
(log NK/Qp)1-ε.


The author's research supported by NSF grant DMS-0650017

Author information

Mathematics Department, Box 1917, Brown University, Providence, RI 02912 USA