Quadratic forms of signature $(2, 2)$ or $(3, 1)$ I: effective equidistribution in quotients of $\mathrm{SL}_4(\mathbb{R})$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908483511648256 |
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| author | Lin, Zuo |
| author_facet | Lin, Zuo |
| contents | We prove an effective equidistribution theorem for orbits of horospherical subgroups of $\mathrm{SO}(2, 2)$ and $\mathrm{SO}(3, 1)$ in quotients of $\mathrm{SL}_4(\mathbb{R})$ with a polynomial error term. In a forthcoming paper, we will use this theorem to prove an effective version of the Oppenheim conjecture for indefinite quadratic forms of signature $(2, 2)$ or $(3, 1)$ with a polynomial error rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06705 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic forms of signature $(2, 2)$ or $(3, 1)$ I: effective equidistribution in quotients of $\mathrm{SL}_4(\mathbb{R})$ Lin, Zuo Dynamical Systems Number Theory 37A17, 28A80, 11E20 We prove an effective equidistribution theorem for orbits of horospherical subgroups of $\mathrm{SO}(2, 2)$ and $\mathrm{SO}(3, 1)$ in quotients of $\mathrm{SL}_4(\mathbb{R})$ with a polynomial error term. In a forthcoming paper, we will use this theorem to prove an effective version of the Oppenheim conjecture for indefinite quadratic forms of signature $(2, 2)$ or $(3, 1)$ with a polynomial error rate. |
| title | Quadratic forms of signature $(2, 2)$ or $(3, 1)$ I: effective equidistribution in quotients of $\mathrm{SL}_4(\mathbb{R})$ |
| topic | Dynamical Systems Number Theory 37A17, 28A80, 11E20 |
| url | https://arxiv.org/abs/2508.06705 |