Quantitative non-divergence and Diophantine approximation on manifolds

2019/06/03 by Dmitry Kleinbock, Victor Beresnevich, Kleinbock, Dmitry +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #11JXX #37A17 #Advanced Mathematical Theories and Applications #Advanced Numerical Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1906.00747

openalex publication_date 2019/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Lattice points in thickened parabolas and rational points near hypersurfaces

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