5 citations · 7 across the 13 of their papers we have counts for
13 papers
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…
Restricted slowly growing digits for infinite iterated function systems
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1
For an infinite iterated function system on with an attractor and for an infinite subset , consider the set \[ \mathbb E…
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…
Transcendence and normality of complex numbers via Hurwitz continued fractions
Felipe García-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…
Liminf approximation sets for abstract rationals
Mumtaz Hussain, Ben Ward
The Jarník-Besicovitch theorem is a fundamental result in metric number theory which concerns the Hausdorff dimension for certain limsup sets. We discuss the analogous problem for…
Metrical properties of exponentially growing partial quotients
Mumtaz Hussain, Nikita Shulga
A fundamental challenge within the metric theory of continued fractions involves quantifying sets of real numbers, when represented using continued fractions, exhibit partial quoti…
Metrical properties of finite product of partial quotients in arithmetic progressions
Mumtaz Hussain, Nikita Shulga
We investigate the dynamics of continued fractions and explore the ergodic behaviour of the products of mixed partial quotients in continued fractions of real numbers. For any func…
Metrical properties of the product of partial quotients with geometric mean in continued fractions
Mumtaz Hussain, Bixuan Li, Nikita Shulga
The theory of uniform Diophantine approximation concerns the study of Dirichlet improvable numbers and the metrical aspect of this theory leads to the study of the product of conse…
Weighted approximation for limsup sets
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1
Theorems of Khintchine, Groshev, Jarník, and Besicovitch in Diophantine approximation are fundamental results on the metric properties of -well approximable sets. These foundati…