ABC implies primitive prime divisors in arithmetic dynamics
نویسندگان
چکیده
منابع مشابه
ABC implies primitive prime divisors in arithmetic dynamics
Let K be a number field, let φ(x) ∈ K(x) be a rational function of degree d > 1, and let α ∈ K be a wandering point such that φ(α) = 0 for all n > 0. We prove that if the abc-conjecture holds for K, then for all but finitely many positive integers n, there is a prime p of K such that vp(φ (α)) > 0 and vp(φ (α)) 0 for all positive integers m < n. Under appropriate ramification hypotheses, we can...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2013
ISSN: 0024-6093
DOI: 10.1112/blms/bdt049