Thue equations and CM-fields
  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. 
Yves Aubry (IMATH, I2M), Dimitrios Poulakis
math.NT