2 citations · 2 across the 6 of their papers we have counts for
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Twisted Diophantine Approximation II: Uniform Theory
Taehyeong Kim, Vasiliy Neckrasov
We develop a general method for uniform twisted metric Diophantine approximation with an arbitrary fixed real matrix. Using all successive minima of the associated diagonal lattice…
Twisted Diophantine Approximation I: Asymptotic Theory
Taehyeong Kim, Vasiliy Neckrasov
We establish an exact zero-one law for twisted Diophantine approximation with an arbitrary fixed real matrix and a positive non-increasing approximation function satisfying dyadic…
Winning property of counterexamples to Uniform Littlewood's Conjecture
Vasiliy Neckrasov, Chengyang Wu, Bohan Yang
In this paper, we prove that the set of counterexamples to the uniform Littlewood's conjecture proposed in Bandi-Fregoli-Kleinbock, that is, the set of pairs of real numbers $(x,y)…
Uniform Diophantine approximation with restrictions via total density of collections of subspaces
Leo Hong, Dmitry Kleinbock, Vasiliy Neckrasov
In 1926 Khintchine introduced a topological argument proving the existence of uncountably many nontrivial singular linear forms of variables. Throughout the years, this…
Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle
Vasiliy Neckrasov
In [Compositio Math. 155 (2019)] Kleinbock and Wadleigh proved a "zero-one law" for uniform inhomogeneous Diophantine approximations. We generalize this statement with arbitrary we…
Metric theory of inhomogeneous Diophantine approximations with a fixed matrix
Nikolay Moshchevitin, Vasiliy Neckrasov
In this paper we develop a metric theory of inhomogeneous Diophantine approximation for the case of a fixed matrix. We use transference principle to connect uniform Diophantine pro…
On Nontrivial Winning and Losing Parameters of Schmidt Games
Vasiliy Neckrasov, Eric Zhan
In this paper we study the classical Schmidt game on two families of sets: one related to frequencies of digits in base- expansions, and one connected to the set of the badly ap…
On Some Properties of Irrational Subspaces
Vasiliy Neckrasov
In this paper we discuss some properties of completely irrational subspaces. We prove that there exist completely irrational subspaces that are badly approximable and, moreover, se…