Integral solutions of a class of Thue equations
Résumé
We obtain polynomial type bounds for the size of the integral solutions of Thue equations $F(X,Y) = m$ defined over a totally real number field $K$, assuming that $F(X,1)$ has at least a non real root and, for every couple of non real conjugate roots $(\alpha, \bar{\alpha})$ of $F(X,1)$, the field $K(\alpha, \bar{\alpha})$ is a CM-field. In case where $F(X,1)$ has also real roots, our approach gives polynomial type bounds that the Baker's method was not able to provide other than exponential bounds.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)