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

Claude Levesque; Michel Waldschmidt

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arXiv · 1505.06656

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

Claude Levesque·Michel Waldschmidt

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Abstract

Let $F$ be an irreducible binary form attached to a number field $K$ of degree $\geq 3$. Let $ε\not\in \{-1, 1\}$ be a totally real unit of $K$. By twisting $F$ with the powers $ε^a$ of $ε$, ($a\in{\mathbf Z}$), 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 $xy\not=0$.

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Claude Levesque, Michel Waldschmidt. 2015-05-25. Familles d'équations de Thue associées à un sous-groupe de rang 1 d'unités totalement réelles d'un corps de nombres. https://arxiv.org/abs/1505.06656

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