Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T08:19:42.835Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  04 December 2007

Roberto M. Avanzi  and
Umberto M. Zannier
Roberto M. Avanzi
Affiliation:
Institut für Experimentelle Mathematik, Universität Essen, Ellernstraße 29, 45326 Essen, Germany. e-mail: mocenigo@exp-math.uni-essen.de
Umberto M. Zannier
Affiliation:
Istituto Universitario di Architettura DCA, Santa Croce 191, 30135 Venice, Italy. e-mail: zannier@dimi.uniud.it
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

diophantine equationsequations admitting rational functions as solutionsreducibility
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 3 , December 2003 , pp. 263 - 295
Copyright
© 2003 Kluwer Academic Publishers