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arXiv · 1908.07165

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

Michael Bersudsky
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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.

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Michael Bersudsky. 2019-08-20. On the distribution of primitive subgroups of $\mathbb{Z}^{d}$ of large covolume. https://arxiv.org/abs/1908.07165

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