Mumtaz Hussain

activity

20092026

most citedHausdorff measure of sets of Dirichlet non-improvable numbers

46 citations · 153 across the 30 of their papers we have counts for

collaborators

Showing 2016Show all

3 papers · 1 filter

math.NT2016

The Hausdorff measure version of Gallagher's theorem -- closing the gap and beyond

Mumtaz Hussain, David Simmons

In this paper we prove an upper bound on the "size" of the set of multiplicatively $ψ$ -approximable points in $R^{d}$ for $d > 1$ in terms of $f$ -dimensional Hausdorff measure.…

math.NT2016★ 3 cited

A note on badly approximabe sets in projective space

Stephen Harrap, Mumtaz Hussain

Recently, Ghosh \& Haynes \cite{HG} proved a Khintchine-type result for the problem of Diophantine approximation in certain projective spaces. In this note we complement their resu…

math.NT2016★ 8 cited

A dichotomy law for the Diophantine properties in $β$ -dynamical systems

Michael Coons, Mumtaz Hussain, Bao-Wei Wang

Let $β > 1$ be a real number and define the $β$ -transformation on $[0, 1]$ by $T_{β} : x \mapsto β x mod 1$ . Further, define $$W_y(T_β,Ψ):=\{x\in [0, 1]:|T_β^nx-y|<Ψ(n) \mbox{ for infinite…

The Hausdorff measure version of Gallagher's theorem -- closing the gap and beyond

A note on badly approximabe sets in projective space

A dichotomy law for the Diophantine properties in β-dynamical systems

A dichotomy law for the Diophantine properties in $β$ -dynamical systems