数苑讲座之二：The measure and fractal properties of Dirichlet non-improvable sets

发布时间：2021-09-17 来源：赢咖3 浏览次数：

Speaker:	吴军	DateTime:	2021年9月20日(周一)下午3:40-4:40
Brief Introduction to Speaker: 吴军教授，华中科技大学。		Place:	6号楼二楼报告厅
Abstract:Dirichlet’s theorem is a fundamental result in metric Diophantine approxima- tion. The improvability of this theorem was first considered by Davenport and Schmidt. After them, Kleinbock and Wadleigh proposed the concept of Dirich- let improvable point formally in 2018 and launched relevant work. Their results show that the improvability of Dirichlet’s theorem is concerned with the growth of the product of the partial quotients. In this talk, we present some results on the size of uniformly Dirichlet non– improvable set, the size of exact Dirichlet non–improvable set and metric prop- erties of the product of the partial quotients in continued fractions.