Variation of Periods Modulo p in Arithmetic Dynamics

Details Variation of Periods Modulo p in Arithmetic Dynamics Variation of Periods Modulo p in Arithmetic Dynamics

2007-07-10

arxiv.org/abs/0707.1505v1

New York Journal of Math. 14 (2008), 601--616 (electronic)

Mathematics

Number Theory

15 pages

Scientific paper

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.

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