Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	廖灵敏，武汉大学
Inviter:
Title:	Diophantine approximation with exponential approximation speed
Language:	Chinese
Time & Venue:	2023.06.15 15:15-16:15 南楼N913
Abstract:	Given a positive real number t>0, we calculate the Hausdorff dimension of the set of the couples (x,y) in the unit square such that \|qx-p_1\|<q^{-t} and \|qy-p_2\|<e^{-q} holds for infinitely many integer triples (q, p_1,p_2) with q>0. Such a study is a generalization of the classical simultaneous Diophantine approximation by replacing the polynomial approximation speed q^{-v} (v>0) for the second coordinate y to the exponential approximation speed e^{-q}. The upper bound of the Hausdorff dimension can be easily deduced from the existing results. For the lower bound, we need to develop the Mass Transference Principle of Wang and Wu (Math. Ann 2021) to incorporate the exponential speed. This is a joint work with Bing Li, Baowei Wang, Sanju Velani and Evgeniy Zorin.