Dmitry Kleinbock

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math.NT2026

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 $n \geq 2$ variables. Throughout the years, this…

math.NT2025

Singularity, weighted uniform approximation, intersections and rates

Dmitry Kleinbock, Nikolay Moshchevitin, Jacqueline Warren +1

A classical argument was introduced by Khintchine in 1926 in order to exhibit the existence of totally irrational singular linear forms in two variables. This argument was subseque…

math.NT2025

Submanifold-genericity of $R^{d}$ -actions and uniform multiplicative Diophantine approximation

Prasuna Bandi, Reynold Fregoli, Dmitry Kleinbock

In this paper, we prove a new ergodic theorem for $R^{d}$ -actions involving averages over dilated submanifolds, thereby generalizing the theory of spherical averages. Our ma…

Uniform Diophantine approximation with restrictions via total density of collections of subspaces

Singularity, weighted uniform approximation, intersections and rates

Submanifold-genericity of Rd-actions and uniform multiplicative Diophantine approximation

Submanifold-genericity of $R^{d}$ -actions and uniform multiplicative Diophantine approximation