5 papers · 1 filter
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…
Weighted approximation for limsup sets
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1
Theorems of Khintchine, Groshev, JarnÃk, and Besicovitch in Diophantine approximation are fundamental results on the metric properties of -well approximable sets. These founda…