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math.NT2026
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 \…
math.NT2026
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 …
math.NT2026
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…