Claude Lévesque

collaborators

3 papers

math.NT2015

A family of Thue equations involving powers of units of the simplest cubic fields

Claude Levesque, Michel Waldschmidt

E. Thomas was one of the first to solve an infinite family of Thue equations, when he considered the forms $F_{n} (X, Y) = X^{3} - (n - 1) X^{2} Y - (n + 2) X Y^{2} - Y^{3}$ and the family of equations…

math.NT2015

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

Let $F$ be an irreducible binary form attached to a number field $K$ of degree $\geq 3$ . Let $ε \neq \in {- 1, 1}$ be a totally real unit of $K$ . By twisting $F$ with the powers $ε^…

math.NT2015

Solving simultaneously Thue equations in the almost totally imaginary case

Claude Levesque, Michel Waldschmidt

Let $α$ be an algebraic number of degree $d \geq 3$ having at most one real conjugate and let $K$ be the algebraic number field $Q (α)$ . For any unit $ε$ of $K$ such that ${…