J. Levesley

activity

20052024

most citedThe mixed Schmidt conjecture in the theory of Diophantine approximation

4 citations · 6 across the 9 of their papers we have counts for

collaborators

10 papers

math.DS2024

Shrinking targets versus recurrence: the quantitative theory

Jason Levesley, Bing Li, David Simmons +1

Let $X = [0, 1]$ , and let $T : X \to X$ be an expanding piecewise linear map sending each interval of linearity to $[0, 1]$ . For $ψ : N \to R_{\geq 0}$ , $x \in X$ , and $N\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…

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…

math.NT2020

A lower bound for the Hausdorff dimension of the set of weighted simultaneously approximable points over manifolds

Victor Beresnevich, Jason Levesley, Benjamin Ward

Given a weight vector $τ = (τ_{1}, \dots, τ_{n}) \in R_{+}^{n}$ with each $τ_{i}$ bounded by certain constraints, we obtain a lower bound for the Hausdorff dimension of the…

math.NT2015

Diophantine Approximation and applications in Interference Alignment

Faustin Adiceam, Victor Beresnevich, Jason Levesley +2

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable…

math.NT2013

A converse to linear independence criteria, valid almost everywhere

Stéphane Fischler, Mumtaz Hussain, Simon Kristensen +1

We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving…