# Thue equations and CM-fields

1 I2M - Institut de Mathématiques de Marseille 2 IMATH - Institut de Mathématiques de Toulon - EA 2134 3 Department of Mathematics

Abstract : We obtain a polynomial type upper bound for the size of the integral solutions of Thue equations $FX,Y = b$ defined over a totally real number field $K$,assuming that $FX,1$ has a root $\alpha$ such that $K\alpha$ is a CM-field.Furthermore, we give an algorithm for the computation of the integral solutions of such an equation.

Mots-clés : CM-fields Thue equations integral solutions

Author: Yves Aubry - Dimitrios Poulakis -

Source: https://hal.archives-ouvertes.fr/