Benjamin Ward

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math.NT2025

A quantitative framework for sets of exact approximation order by rational numbers

Simon Baker, Benjamin Ward

In this paper we study a quantitative notion of exactness within Diophantine approximation. Given $Ψ : (0, \infty) \to (0, \infty)$ and $ω : (0, \infty) \to (0, 1)$ satisfying $\lim_{q\to\in…

math.NT2023

The dimension of the set of $ψ$ -badly approximable points in all ambient dimensions; on a question of Beresnevich and Velani

Henna Koivusalo, Jason Levesley, Benjamin Ward +1

Let $ψ : N \to [0, \infty)$ , $ψ (q) = q^{- (1 + τ)}$ and let $ψ$ -badly approximable points be those vectors in $R^{d}$ that are $ψ$ -well approximable, but not $c ψ$ -well ap…

A quantitative framework for sets of exact approximation order by rational numbers

The dimension of the set of ψ-badly approximable points in all ambient dimensions; on a question of Beresnevich and Velani

The dimension of the set of $ψ$ -badly approximable points in all ambient dimensions; on a question of Beresnevich and Velani