数学研究所
学术报告
动力系统讨论班
Speaker: 李兵 教授（华南理工大学）
Inviter: 何伟鲲
Title: Hausdorff measures and dimensions for the well approximable sets in missing digit sets
Language: Chinese
Time&Venue: 2025.6.30（周一）10:00-11:00 & N913
Abstract: Let b≥3 be an integer and C(b,D) be the set of real numbers
in [0,1] whose base b -expansion only consists of digits in a set S⊂{0,1,,⋯,b-1}.
Motivated by Mahler’s problem, we consider how close can numbers inC(b,D)
be approximated by rational numbers with denominators being powers of some integer t.
Some Hausdorff measure and dimension results will be given in the talk.
The phenomena are different for the following three cases of b
and t: (i) multiplicatively dependent; (ii) multiplicatively independent but have the
same prime divisors; (iii) the left case.
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