Polynomial effective density in quotient of $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929323907219456 |
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| author | Lin, Zuo |
| author_facet | Lin, Zuo |
| contents | We prove an effective density theorem with polynomial error rate for orbits of upper triangular subgroup of $\mathrm{SL}_2(\mathbb{Q}_p)$ in $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$ for prime number $p > 3$. The proof is based on the use of Margulis function, a restricted projection theorem on $\mathbb{Q}_p^3$, and spectral gap of the ambient space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial effective density in quotient of $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$ Lin, Zuo Dynamical Systems 37A17, 37A25 We prove an effective density theorem with polynomial error rate for orbits of upper triangular subgroup of $\mathrm{SL}_2(\mathbb{Q}_p)$ in $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$ for prime number $p > 3$. The proof is based on the use of Margulis function, a restricted projection theorem on $\mathbb{Q}_p^3$, and spectral gap of the ambient space. |
| title | Polynomial effective density in quotient of $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$ |
| topic | Dynamical Systems 37A17, 37A25 |
| url | https://arxiv.org/abs/2404.13931 |