Non-spectrality of Moran measures with consecutive digits

Ya-Li Zheng, Wen-Hui Ai

Let $\rho =(\frac{p}{q}{)}^{\frac{1}{r}}<1$ for some $p,q,r\in \mathbb{N}$ with $(p,q)=1$ and ${\mathcal{D}}_n=\{0,1,\cdot \cdot \cdot ,N_n-1\}$, where $N_n$ is prime for all $n\in\mathb…