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arXiv · 2103.05163

Equidistribution of rational subspaces and their shapes

Menny Aka·Andrea Musso·Andreas Wieser
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Abstract

To any $k$-dimensional subspace of $\mathbb Q^n$ one can naturally associate a point in the Grassmannian ${\rm Gr}_{n,k}(\mathbb R)$ and two shapes of lattices of rank $k$ and $n-k$ respectively. These lattices originate by intersecting the $k$-dimensional subspace with the lattice $\mathbb Z^n$. Using unipotent dynamics we prove simultaneous equidistribution of all of these objects under a congruence conditions when $(k,n) \neq (2,4)$.

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Menny Aka, Andrea Musso, Andreas Wieser. 2021-03-09. Equidistribution of rational subspaces and their shapes. https://doi.org/10.1017/etds.2023.107

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