Familles d'équations de Thue associées à un sous-groupe de rang 1 d'unités totalement réelles d'un corps de nombres

Abstract

Let $F$ be an irreducible binary form attached to a number field $K$ of degree $\ge 3$. Let $\epsilon \notin \{-1,1\}$ be a totally real unit of $K$. By twisting $F$ with the powers ${\epsilon }^a$ of $\epsilon$, ($a\in \mathbf{Z}$), we obtain an infinite family $F_a$ of binary forms. Let $m\in \mathbf{Z}$. We give an effective bound for $\max \{|a|,\log |x|,\log |y|\}$ when $a,x,y$ are rational integers satisfying $F_a(x,y)=m$ with $xy\ne 0$.

in French, CRM collection "Contemporary Mathematics", AMS, to appear