5 citations · 10 across the 7 of their papers we have counts for
8 papers
Zero-one laws for uniform approximation via Gaussian and Eisenstein integers
René Pfitscher, Anurag Rao, Shucheng Yu +1
We establish two distinct zero-one laws for the uniform Diophantine approximation of complex numbers by quotients of Gaussian integers and by quotients of Eisenstein integers. Usin…
Constructing bounded orbits of special types on homogeneous spaces
Manfred Einsiedler, Dmitry Kleinbock, Anurag Rao
Let be a quotient of a real Lie group by a non-uniform lattice. Consider a one-parameter subgroup of that is -diagonalizable over …
K-divergent lattices
Guy Lachman, Anurag Rao, Uri Shapira +1
We introduce a novel concept in topological dynamics, referred to as -divergence, which extends the notion of divergent orbits. Motivated by questions in the theory of inhomogen…
A dichotomy phenomenon for Bad minus normed Dirichlet
Dmitry Kleinbock, Anurag Rao
Given a norm on , the set of -Dirichlet improvable numbers was defined and studied in the papers of Andersen-Duke (Acta Arith. 2021) and Kleinb…
Weighted uniform Diophantine approximation of systems of linear forms
Dmitry Kleinbock, Anurag Rao
Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability…
Abundance of Dirichlet-improvable pairs with respect to arbitrary norms
Dmitry Kleinbock, Anurag Rao
In a recent paper of Akhunzhanov and Shatskov the two-dimensional Dirichlet spectrum with respect to Euclidean norm was defined. We consider an analogous definition for arbitrary n…
Critical loci of convex domains in the plane
Dmitry Kleinbock, Anurag Rao, Srinivasan Sathiamurthy
Let be a bounded convex domain in symmetric about the origin. The critical locus of is defined to be the (non-empty compact) set of lattices in $\mathbb{…
A zero-one law for uniform Diophantine approximation in Euclidean norm
Dmitry Kleinbock, Anurag Rao
We study a norm sensitive Diophantine approximation problem arising from the work of Davenport and Schmidt on the improvement of Dirichlet's theorem. Its supremum norm case was rec…