Thue equations and CM-fields

Abstract

We obtain a polynomial type upper bound for the size of the integral solutions of Thue equations $F(X,Y)=b$ defined over a totally real number field $K$, assuming that $F(X,1)$ 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.