46 citations · 153 across the 30 of their papers we have counts for
33 papers
Well and badly approximable sets, and rapid winning
Mumtaz Hussain, David Simmons
The set of -approximable numbers, , has genuinely fractional Hausdorff dimension, whereas the set of inhomogeneously badly approximable numbers, $\Bad^γ$, has ful…
Dual -adic Diophantine approximation on manifolds
Mumtaz Hussain, Johannes Schleischitz, Benjamin Ward
The Generalised Baker-Schmidt Problem (1970) concerns the Hausdorff measure of the set of -approximable points on a nondegenerate manifold. Beresnevich-Dickinson-Velani (in 2006…
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 be matrix of rea…
Metrical properties of weighted products of consecutive Lüroth digits
Adam Brown-Sarre, Gerardo González Robert, Mumtaz Hussain
The Lüroth expansion of a real number is the series \[ x= \frac{1}{d_1} + \frac{1}{d_1(d_1-1)d_2} + \frac{1}{d_1(d_1-1)d_2(d_2-1)d_3} + \cdots, \] with $d_j\in\mathbb{…
Metrical properties of Hurwitz Continued Fractions
Yann Bugeaud, Gerardo Gonzalez Robert, Mumtaz Hussain
We develop the geometry of Hurwitz continued fractions, a major tool in understanding the approximation properties of complex numbers by ratios of Gaussian integers. Based on a tho…
The Baker-Schmidt problem for dual approximation and some classes of functions
Mumtaz Hussain, Johannes Schleischitz
The Generalised Baker-Schmidt Problem (1970) concerns the Hausdorff -measure of the set of -approximable points on a nondegenerate manifold. We refine and extend our previous…