On the distribution of primitive subgroups of ${\mathbb{Z}}^d$ of large covolume

Abstract

We prove existence and compute the limiting distribution of the image of rank-$\left(d-1\right)$ primitive subgroups of ${\mathbb{Z}}^d$ of large covolume in the space $X_{d-1,d}$ of homothety classes of rank-$\left(d-1\right)$ discrete subgroups of ${\mathbb{R}}^d$. This extends a theorem of Aka, Einsiedler and Shapira.

Cited by in corpus (1)

• Equidistribution of rational subspaces and their shapes