Khintchine's singular systems and their applications
Nikolay G. Moshchevitin
TL;DR
This survey reviews historical and recent results on Khintchine's singular matrices and explores their applications in Diophantine approximation, highlighting developments in this mathematical area.
Contribution
It compiles and discusses both old and new findings on Khintchine's singular matrices and their role in Diophantine approximation, providing a comprehensive overview.
Findings
Summary of classical and recent results on singular matrices
Applications of singular matrices in Diophantine approximation
Future research directions in the field
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.
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