Title：On the irrationality exponent of real numbers with low complexity expansions

Speaker：Dong Han Kim (Professor，Dongguk University, South Korea)

Time: Nov 6,2026,10:30-11:30

Venue: Room 224, Building No. 4, Wushan Campus

Abstract: 

Let $\xi$ be a real number and $b \geq 2$ be an integer. We study the relationship between the irrationality exponent of $\xi$ and the subword complexity of the $b$-ary expansion of $\xi$. If the irrationality exponent of $\xi$ is greater than 2, then the subword complexity of the $b$-ary expansion of $\xi$ cannot be too small. 

In this talk, we show that the limit superior of the subword complexity, normalized by the subword length $n$, is at least 4/3 for any $\xi$ whose irrationality exponent is greater than 2.

This is joint work with Yann Bugeaud and Hajime Kaneko.