Abstract

Diophantine approximation concerns how well a real number can be approximated by rationals and its generalization. Dirichlet’s theorem and Minkowski’s theorem are the two most fundamental results in this aspects which initial the study for the metric theory of limsup sets generated by balls and generated by rectangles. The theory for the first limusp set has been well established since the landmark work of Mass transference principle established by Beresenevich & Velani. In this talk, we will discuss the recent progress on the latter limsup set.