Rational points in Cantor sets and spectral eigenvalue problem for self-similar spectral measures

Derong Kong, Kun Li, Zhiqiang Wang

Given $q\in {\mathbb{N}}_{\ge 3}$ and a finite set $A\subset \mathbb{Q}$, let $$K(q,A)=\{\sum _{i=1}^{\infty }\frac{a_i}{q^i}:a_i\in A\forall i\in \mathbb{N}\}.$$ For…