6 citations · 8 across the 2 of their papers we have counts for
10 papers
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…
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 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 twisted inhomogeneous Diophantine approximation
Mumtaz Hussain, Benjamin Ward
We prove a multidimensional weighted analogue of the well-known theorem of Kurzweil (1955) in the metric theory of inhomogeneous Diophantine approximation. Let be matrix of rea…