Arithmetic structure of the exceptional set of projections

Changhao Chen, Zhengyan Miao

We study the arithmetic structure of the exceptional set of projections. For any bounded subset $E\subset {\mathbb{R}}^d$, let $$\hat{I}\text{c◯}=\{\hat{I}¾\in \mathbb{R}:{\dim }_B(E+\hat{I}¾E)={\dim }_{B}E\}.$$…