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Density of the multidimensional Lagrange spectrum
Dmitry Kleinbock
The Lagrange spectrum is a classical object in number theory, defined as the set of values of where runs through irratio…
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…
Submanifold-genericity of -actions and uniform multiplicative Diophantine approximation
Prasuna Bandi, Reynold Fregoli, Dmitry Kleinbock
In this paper, we prove a new ergodic theorem for -actions involving averages over dilated submanifolds, thereby generalizing the theory of spherical averages. Our ma…
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…
Inhomogeneous Diophantine approximation for generic homogeneous functions
Dmitry Kleinbock, Mishel Skenderi
The present paper is a sequel to [Monatsh.~Math.\ {\bf 194} (2021), 523--554] in which results of that paper are generalized so that they hold in the setting of inhomogeneous Dioph…