Quantitative non-divergence and Diophantine approximation on manifolds
Number Theory
2020-08-24 v2 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1906.00747,
title = {Quantitative non-divergence and Diophantine approximation on manifolds},
author = {Dmitry Kleinbock and Victor Beresnevich},
journal= {arXiv preprint arXiv:1906.00747},
year = {2020}
}
Comments
32 pages, added references and new results