Dr Mumtaz Hussain


Author: MohidZaman

Metrical properties of Hurwitz Continued Fractions

Yann Bugeaud, Gerardo Gonzalez Robert and I have uploaded a paper to the arXiv https://arxiv.org/abs/2306.08254 concerning the metrical properties of Hurwitz Continued Fraction expansions. We develop the geometry of Hurwitz continued fractions – a major tool in understanding the approximation properties of complex numbers by ratios of Gaussian integers. We

Weighted approximation for limsup sets

We just uploaded to the arXiv a paper concerning “weighted approximation for limsup sets” jointly with Gerardo Gonzalez Robert, Nikita Shulga, and Ben Ward. The link to the arXiv is https://arxiv.org/abs/2308.16603. Theorems of Khintchine, Groshev, Jarník, and Besicovitch in Diophantine ap- proximation are fundamental results on the metric properties of

A general principle for Hausdorff measure

We introduce a general principle for studying the Hausdorff measure of limsup sets. A consequence of this principle is the well-known Mass Transference Principle of Beresnevich and Velani (2006). https://arxiv.org/pdf/1808.02135.pdf The main result is as follows. \begin{theorem}[Hussain-Simmons, 2018]\label{HS:thm} Fix , let be a sequence of open sets in an Ahlfors -regular