The equation f(X) = f(Y) in rational functions X = X(t), y = Y(t)

Roberto M. Avanzi, Umberto M. Zannier

Research output: Contribution to journalArticlepeer-review


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 ε K.

Original languageEnglish
Pages (from-to)263-295
Number of pages33
JournalCompositio Mathematica
Issue number3
StatePublished - Dec 2003
Externally publishedYes


  • Diophantine equations
  • Equations admitting rational functions as solutions
  • Reducibility

ASJC Scopus subject areas

  • Algebra and Number Theory


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