Khintchine's singular systems and their applications

Abstract

This paper is a survey of old and recent results related to Khintichine's singular matrices and their applications in the theory of Diophantine approximations. The paper is written in Russian. English version should appear in "Russian Mathematical Surveys" in the beginning of 2010.

Paper in Russian, summary in English

Cited by in corpus (4)

• A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation
• Geometry of Diophantine exponents
• On Some Properties of Irrational Subspaces
• Singularity, weighted uniform approximation, intersections and rates