Rational points in Cantor sets in the complex plane

Wenxia Li, Zhiqiang Wang, Jiuzhou Zhao

Let $K$ be an imaginary quadratic field and let ${\mathcal{O}}_K$ be the ring of algebraic integers of $K$. For $\alpha \in {\mathcal{O}}_K$ with $|\alpha |>1$, define \[ \mathcal{D}_α= \bigcup_…