Uniform Boundedness of S-units in Arithmetic Dynamics
نویسندگان
چکیده
Let K be a number field and let S be a finite set of places of K which contains all the Archimedean places. For any φ(z) ∈ K(z) of degree d ≥ 2 which is not a d-th power in K(z), Siegel’s theorem implies that the image set φ(K) contains only finitely many S-units. We conjecture that the number of such S-units is bounded by a function of |S| and d (independently of K, S and φ). We prove this conjecture for several classes of rational functions, and show that the full conjecture follows from the Bombieri–Lang conjecture.
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