报告人：Mumtaz Hussain博士  La Trobe University

报告题目: Metrical results for the sets of Dirichlet non-improvable numbers

报告摘要： Let $\psi:\mathbb R_+\to\mathbb R_+$ be a non-increasing function. A real number $x$ is said to be $\psi$-Dirichlet improvable if it admits an improvement to Dirichlet's theorem in the sense that the system $$|qx-p|< \, \psi(t) \ \ {\text{and}} \ \ |q|<t$$ has a non-trivial integer solution for all large enough $t$.  In this talk, I will explain that the Hausdorff measure of the set of  $\psi$-Dirichlet non-improvable numbers obey a zero-infinity law for a large class of dimension functions.

报告时间：2017年7月10日(星期一)下午14：30-15：15

报告地点: 科技楼南楼602室