Benjamin C. Ward

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20172022

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math.NT2022

Weighted approximation in higher-dimensional missing digit sets

Demi Allen, Benjamin Ward

In this note, we use the mass transference principle for rectangles, recently obtained by Wang and Wu (Math. Ann., 2021), to study the Hausdorff dimension of sets of "weighted $Ψ$ -…

math.NT2021

Counting rational points close to $p$ -adic integers and applications in Diophantine approximation

Benjamin Ward

We find upper and lower bounds on the number of rational points that are $ψ$ -approximations of some $n$ -dimensional $p$ -adic integer. Lattice point counting techniques are used to…

math.NT2021

Simultaneous p-adic Diophantine approximation

Victor Beresnevich, Jason Levesley, Benjamin Ward

The goal of this paper is to develop the theory of weighted Diophantine approximation of rational numbers to $p$ -adic numbers. Firstly, we establish complete analogues of Khintchin…

Weighted approximation in higher-dimensional missing digit sets

Counting rational points close to p-adic integers and applications in Diophantine approximation

Simultaneous p-adic Diophantine approximation

Counting rational points close to $p$ -adic integers and applications in Diophantine approximation