Prime divisors in polynomial orbits over function fields

preprint2015arXivOpen access

Abstract

Given a polynomial ϕϕ over a global function field KK and a wandering base point b∈Kb\in K, we give a geometric condition on ϕϕ ensuring the existence of primitive prime divisors for almost all points in the orbit Oϕ(b):={ϕn(b)}n≥0\mathcal{O}_ϕ(b):=\{ϕ^n(b)\}_{n\geq0}

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