Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915399770046464 |
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| author | Lindenstrauss, Elon Mohammadi, Amir Wang, Zhiren Yang, Lei |
| author_facet | Lindenstrauss, Elon Mohammadi, Amir Wang, Zhiren Yang, Lei |
| contents | We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2.
As an application, inspired by the results of Eskin, Margulis and Mozes, we establish quantitative results regarding the distribution of values of an indefinite ternary quadratic form at integer points, giving in particular an effective and quantitative proof of the Oppenheim Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms Lindenstrauss, Elon Mohammadi, Amir Wang, Zhiren Yang, Lei Dynamical Systems Number Theory We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2. As an application, inspired by the results of Eskin, Margulis and Mozes, we establish quantitative results regarding the distribution of values of an indefinite ternary quadratic form at integer points, giving in particular an effective and quantitative proof of the Oppenheim Conjecture. |
| title | Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2503.21064 |