5 citations · 7 across the 13 of their papers we have counts for
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The Cartesian product of exact approximation sets
Jing Guo, Mumtaz Hussain, Bixuan Li +1
We determine the Hausdorff and packing dimensions of Cartesian products of one-dimensional exact approximation sets. Our main result establishes the exact-approximation counterpart…
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…
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…
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…
Complex numbers with a prescribed order of approximation and Zaremba's conjecture
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga
Given with being a positive integer, we can represent any complex number as a power series in with coefficients in . We prove th…