Effective equidistribution of translates of tori in arithmetic homogeneous spaces and applications
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917355065442304 |
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| author | Sarkar, Pratyush |
| author_facet | Sarkar, Pratyush |
| contents | Let $Γ< G$ be an arithmetic lattice in a noncompact connected semisimple real algebraic group. For many such $G$ of rank at most $2$, in particular $G = \operatorname{SL}_3(\mathbb R)$, we prove effective equidistribution of large translates of tori in $G/Γ$. As an application, we obtain an asymptotic counting formula with a power saving error term for integral $3 \times 3$ matrices with a specified characteristic polynomial. These effectivize celebrated theorems of Eskin-Mozes-Shah. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective equidistribution of translates of tori in arithmetic homogeneous spaces and applications Sarkar, Pratyush Dynamical Systems Number Theory 11N45, 22E40, 37A17, 37A25 Let $Γ< G$ be an arithmetic lattice in a noncompact connected semisimple real algebraic group. For many such $G$ of rank at most $2$, in particular $G = \operatorname{SL}_3(\mathbb R)$, we prove effective equidistribution of large translates of tori in $G/Γ$. As an application, we obtain an asymptotic counting formula with a power saving error term for integral $3 \times 3$ matrices with a specified characteristic polynomial. These effectivize celebrated theorems of Eskin-Mozes-Shah. |
| title | Effective equidistribution of translates of tori in arithmetic homogeneous spaces and applications |
| topic | Dynamical Systems Number Theory 11N45, 22E40, 37A17, 37A25 |
| url | https://arxiv.org/abs/2506.06948 |