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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…
Radical bound for Zaremba's conjecture
Nikita Shulga
Famous Zaremba's conjecture (1971) states that for each positive integer , there exists positive integer , coprime to , such that if you expand a fraction $a…
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…
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…
Difference of irrationality measure functions
Viktoria Rudykh, Nikita Shulga
For an irrational number we consider its irrationality measure function It is known for all irrational…