Irrationality exponents and Hankel determinants
主 题: Irrationality exponents and Hankel determinants
报告人: Prof. Guo-Niu Han (CNRS法国国家科研中心)
时 间: 2017-06-05 10:00-11:00
地 点: 理科一号楼1493
In 1998, Allouche, Peyriere, Wen and Wen established a congruence relation between the Hankel determinants of theThue-Morse sequence, and proved that all the Hankel determinants of the Thue-Morse sequence are nonzero. This property allowed Bugeaud to prove thatthe irrationality exponents of the Thue-Morse-Mahler numbers are exactly 2. Similar properties for other sequences were derived by Coons, Guo, Wu, Wen by using the same method. In this talk, we present several other proofs and methods. In particular, a one-page proof and a computer assisted proof. We show that the irrationality exponents of large classes of automatic numbers and Mahler numbers are exactly equal to 2.
