 

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 


Abstract
Let ϕ:V→ V be a selfmorphism 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 m_{p}(ϕ,P) be the size of the
ϕorbit 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 m_{p}(ϕ,P) is larger than
(log N_{K/Q}p)^{1ε}.


Acknowledgements
The author's research supported by NSF grant DMS0650017


Author information
Mathematics Department, Box 1917, Brown University, Providence, RI 02912 USA
jhs@math.brown.edu

