The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t)

The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t)

We determine all the complex polynomials f(X) such that, for two suitable distinct, nonconstant rational functions g(t) and h(t), the equality f(g(t)) = f(h(t)) holds. This extends former results of Tverberg, and is a contribution to the more general question of determining the polynomials f(X) over...

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Veröffentlicht in:Compositio mathematica 2003-12, Vol.139 (3), p.263-295
Hauptverfasser: Avanzi, Roberto M., Zannier, Umberto M.
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container_title Compositio mathematica
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Zannier, Umberto M.
description We determine all the complex polynomials f(X) such that, for two suitable distinct, nonconstant rational functions g(t) and h(t), the equality f(g(t)) = f(h(t)) holds. This extends former results of Tverberg, and is a contribution to the more general question of determining the polynomials f(X) over a number field K such that f(X) − λ has at least two distinct K-rational roots for infinitely many λ ∈ K.
doi_str_mv 10.1023/B:COMP.0000018136.23898.65
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title The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t)
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