Benjamin Ward

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

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…

math.NT2023

Liminf approximation sets for abstract rationals

Mumtaz Hussain, Ben Ward

The Jarník-Besicovitch theorem is a fundamental result in metric number theory which concerns the Hausdorff dimension for certain limsup sets. We discuss the analogous problem for…

math.NT2023

Weighted twisted inhomogeneous Diophantine approximation

Mumtaz Hussain, Benjamin Ward

We prove a multidimensional weighted analogue of the well-known theorem of Kurzweil (1955) in the metric theory of inhomogeneous Diophantine approximation. Let $A$ be matrix of rea…

math.NT2023★ 1 cited

Bad is null

Victor Beresnevich, Shreyasi Datta, Anish Ghosh +1

In this paper we develop a general framework of badly approximable points in a metric space $X$ equipped with a $σ$ -finite doubling Borel regular measure $μ$ . We establish that und…

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

Liminf approximation sets for abstract rationals

Weighted twisted inhomogeneous Diophantine approximation

Bad is null

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