On the Sets of Complex Numbers with Specific Approximation Order

Date: 
Friday, 29 July, 2022 - 14:30 - 15:30
Venue: 
LSB 222
Seminar Type: 
Seminar
Speaker Name: 
Prof. Ying XIONG
Affiliation: 
South China University of Technology
Abstract: 

In this talk, we introduce some metric results on the Diophantine approximation of complex numbers. More precisely, let ψ be a positive non-increasing function that tends to zero at infinity, we obtain the Hausdorff and packing dimensions of the sets of ψ-well approximable and ψ-exact approximable complex numbers. These results can be viewed as the analogues of the classical Jarník Theorem in the real case.