On the Eigen-Falconer theorem in ${\mathbb{R}}^d$

Wenxia Li, Zhiqiang Wang, Jiayi Xu

In this paper, we study the analogous Erdős similarity conjecture in higher dimensions and generalize the Eigen-Falconer theorem. We show that if $A=\{\boldsymbol{x}_n\}_{n=1}^\in…