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1 results

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

  • Roberto M. Avanzi, Umberto M. Zannier
  • Journal:
    Compositio Mathematica / Volume 139 / Issue 3 / December 2003
    Published online by Cambridge University Press:
    04 December 2007, pp. 263-295
    Print publication:
    December 2003
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  • 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.