5 citations · 10 across the 16 of their papers we have counts for
16 papers
Simultaneous Diophantine approximation on the three-dimensional Veronese curve: the complete Hausdorff dimension story
Dmitry Badziahin, Nikita Shulga
We determine the Hausdorff dimension of the intersection of the set of simultaneously -well approximable points with the Veronese curve $\mathcal V_3 \subset \…
The uniform Littlewood conjecture fails on a set of positive Hausdorff dimension
Nikita Shulga
The uniform Littlewood conjecture (ULC), introduced by Bandi, Fregoli and Kleinbock, asserts in the two-number case that …
Nine-distance theorem and growth of best-approximation denominators
Nikita Shulga
We prove a nine-distance theorem for Kronecker sequences on flat three-tori. That is, we show that among the first orbit points, at most nine distinct positive nearest-neighbou…
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…
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…
A Hausdorff dimension analysis of sets with the product of consecutive vs single partial quotients in continued fractions
Mumtaz Hussain, Bixuan Li, Nikita Shulga
We present a detailed Hausdorff dimension analysis of the set of real numbers where the product of consecutive partial quotients in their continued fraction expansion grow at a cer…
Derivative of the iterations of Minkowski question mark function in special points
Nikita Shulga
For the Minkowski question mark function we consider derivative of the function . Apart from obvious cases (rational numb…
Rational approximations to two irrational numbers
Nikita Shulga
For real we consider the irrationality measure function , where - distance to the nearest integer.…
Diophantine properties of fixed points of Minkowski question mark function
Dmitry Gayfulin, Nikita Shulga
We consider irrational fixed points of the Minkowski question mark function , that is irrational solutions of the equation . It is easy to see that there exist at l…