Gaussian rational numbers in Cantor sets in the complex plane

Yu-Feng Wu

Given ${\hat{I}}^2\in \mathbb{Z}[i]$ with $|{\hat{I}}^2|>1$ and a finite set $D\subset \mathbb{Q}(i)$, let \[K_{β, D}=\left\{\sum_{j=1}^{\infty}\frac{d_j}{β^j}: d_j\in D, \forall j\geq 1\right\}.\]…