Ramification in iterated towers for rational functions
نویسندگان
چکیده
Abstract. Let φ(x) be a rational function of degree > 1 defined over a number field K and let Φn(x, t) = φ (x) − t ∈ K(x, t) where φ(x) is the nth iterate of φ(x). We give a formula for the discriminant of the numerator of Φn(x, t) and show that, if φ(x) is postcritically finite, for each specialization t0 of t to K, there exists a finite set St0 of primes of K such that for all n, the primes dividing the discriminant are contained in St0 .
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تاریخ انتشار 2009