6 papers
Measure theoretic properties of large products of consecutive partial quotients
Adam Brown-Sarre, Gerardo González Robert, Mumtaz Hussain
The theory of uniform approximation of real numbers motivates the study of products of consecutive partial quotients in regular continued fractions. For any non-decreasing positive…
Approximation by uniformly distributed sequences
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1
We consider approximation properties of real points by uniformly distributed sequences. Under some assumptions on the approximation functions, we prove a Khintchine-type - di…
Weighted approximation for limsup sets
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1
Theorems of Khintchine, Groshev, JarnÃk, and Besicovitch in Diophantine approximation are fundamental results on the metric properties of -well approximable sets. These founda…
A note on limsup sets of annuli
Mumtaz Hussain, Benjamin Ward
We consider the set of points in infinitely many max-norm annuli centred at rational points in . We give JarnÃk-Besicovitch type theorems for this set in terms of H…
On the Folklore set and Dirichlet spectrum for matrices
Mumtaz Hussain, Johannes Schleischitz, Benjamin Ward
We study the Folklore set of Dirichlet improvable matrices in which are neither singular nor badly approximable. We prove the non-emptiness for all positive…
Transcendence and normality of complex numbers via Hurwitz continued fractions
Felipe GarcÃa-Ramos, Gerardo González Robert, Mumtaz Hussain
We study the topological, dynamical, and descriptive set theoretic properties of Hurwitz continued fractions. Hurwitz continued fractions associate an infinite sequence of Gaussian…