Equidistribution of rational subspaces and their shapes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866915025013178368 |
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| author | Aka, Menny Musso, Andrea Wieser, Andreas |
| author_facet | Aka, Menny Musso, Andrea Wieser, Andreas |
| contents | 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 $(k,n) \neq (2,4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_05163 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Equidistribution of rational subspaces and their shapes Aka, Menny Musso, Andrea Wieser, Andreas Number Theory Dynamical Systems 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 $(k,n) \neq (2,4)$. |
| title | Equidistribution of rational subspaces and their shapes |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2103.05163 |