Towards a zero-one law for improvements to Dirichlet's approximation theorem

Abstract

In this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was introduced by Kleinbock and Wadleigh in 2018 and generalizes the classical notion of a matrix being Dirichlet-improvable. In particular, we prove a partial zero-one law for the Lebesgue measure of the set of $\psi$-Dirichlet matrices. Joint with Dmitry Kleinbock and Andreas Strömbergsson.

于树澄研究方向

（1）丢番图逼近

（2）齐性动力系统

https://faculty.ustc.edu.cn/yushucheng/zh_CN/index/661256/list/index.htm