2 citations · 3 across the 12 of their papers we have counts for
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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…
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…