D. Roy

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20242026

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math.NT2026

Extremal numbers and multi-parametric geometry of numbers

Damien Roy

We study weighted simultaneous rational approximation to points of the form $(1, I^¾, I^¾^{2})$ , for a class of extremal real numbers $I^¾$ , within the framework of multi-parametric geome…

math.NT2025

Best versus uniform Diophantine approximatio

Martin Rivard-Cooke, Damien Roy

Let $0 < m < n$ be integers, and let $K_{w}$ denote the completion of a number field $K$ at a non-trivial place $w$ . For each non-zero $u \in K_{w}^{n}$ , let $I ¨ _{m - 1} (u)$ d…

math.NT2024

On simultaneous approximation to a real number, its square, and its cube, II

Damien Roy

In a previous paper with the same title, we gave an upper bound for the exponent of uniform rational approximation to a quadruple of $Q$ -linearly independent real numbers…