Primitive Divisors in Arithmetic Dynamics

Details Primitive Divisors in Arithmetic Dynamics Primitive Divisors in Arithmetic Dynamics

2007-07-17

arxiv.org/abs/0707.2505v2

Proc. Camb. Philos. Soc. 146 #2 (2009), 289--302

Mathematics

Number Theory

Version 2 is substantial revision. The proof of the main theorem has been simplified and strengthened. (16 pages)

Scientific paper

Let F(z) be a rational function in Q(z) of degree at least 2 with F(0) = 0 and such that F does not vanish to order d at 0. Let b be a rational number having infinite orbit under iteration of F, and write F^n(b) = A_n/B_n as a fraction in lowest terms. We prove that for all but finitely many n > 0, the numerator A_n has a primitive divisor, i.e., there is a prime p such that p divides A_n and p does not divide A_i for all i < n. More generally, we prove an analogous result when F is defined over a number field and 0 is a periodic point for F.

Affiliated with

Also associated with

No associations

Rating

Primitive Divisors in Arithmetic Dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Primitive Divisors in Arithmetic Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Primitive Divisors in Arithmetic Dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-562767