| 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.
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