Dmitry Kleinbock, Victor Beresnevich
Published 2019-06-03Version 1
The goal of this survey is to discuss the Quantitative non-Divergence estimate on the space of lattices and present a selection of its applications. The topics covered include extremal manifolds, Khintchine-Groshev type theorems, rational points lying close to manifolds and badly approximable points on manifolds. The main emphasis is on the role of the Quantitative non-Divergence estimate in the aforementioned topics within the theory of Diophantine approximation, and therefore this paper should not be regarded as a comprehensive overview of the area.
Equidistribution on homogeneous spaces and the distribution of approximates in Diophantine approximation
Weak admissibility, primitivity, o-minimality, and Diophantine approximation
Diophantine approximation on subspaces of $\mathbb{R}^n$ and dynamics on homogeneous spaces
![QR code for arXiv:1906.00747 [math.NT]](http://oss.arxitics.com/images/favicon.svg)