4 papers
Distribution of points near the origin in the -dimensional Lagrange spectrum
Benjamin Ward
We develop a new framework, inspired by Schmidt's games, to study the Lagrange spectrum for simultaneous Diophantine approximation in dimension . We show the Hausdorff dim…
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…
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 Jarník-Besicovitch type theorems for this set in terms of Ha…
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…