The measure and fractal properties of Dirichlet non-improvable sets
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题目：The measure and fractal properties of Dirichlet non-improvable sets
时间: 2019年11月29日 上午10:00-11:00
摘要：Dirichlet’s theorem is a fundamental result in metric Diophantine approximation. The improvability of this theorem was first considered by Davenport and Schmidt. After them, Kleinbock and Wadleigh proposed the concept of Dirichlet 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 properties of the product of the partial quotients in continued fractions.