C. Levesque

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20152018

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math.NT2018

Linear recurrence sequences and twisted binary forms

Claude Levesque, Michel Waldschmidt

Let $\prod_{i = 1}^{d} (X - α_{i} Y) \in C [X, Y]$ be a binary form and let $ε_{1}, \dots, ε_{d}$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-α_…

math.NT2017

Representation of integers by cyclotomic binary forms

Etienne Fouvry, Claude Levesque, Michel Waldschmidt

The homogeneous form $Φ_{n} (X, Y)$ of degree $φ (n)$ which is associated with the cyclotomic polynomial $ϕ_{n} (X)$ is dubbed a {\it cyclotomic binary form}. A positive integer $m \geq 1$ i…

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

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 ${…