Geometric and arithmetic aspects of approximation vectors

Uri Shapira, Barak Weiss

Let $\hat{I}¸\in {\mathbb{R}}^d$. We associate three objects to each approximation $(p,q)\in {\mathbb{Z}}^d\times \mathbb{N}$ of $\hat{I}¸$: the projection of the lattice ${\mathbb{Z}}^{d+1}$ to the…