Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910118281478144 |
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| author | Strömbergsson, Andreas Södergren, Anders Vishe, Pankaj |
| author_facet | Strömbergsson, Andreas Södergren, Anders Vishe, Pankaj |
| contents | Let $G=\SL(2,\R)\ltimes(\R^2)^{k}$, let $Γ$ be a congruence subgroup of $\SL(2,\Z)\ltimes(\Z^2)^{k}$, and let $u_{\R}=(u_x)_{x\in\R}$ be the one-parameter subgroup of $G$ given by $u_x=\left(\matr 1x01,0\right)$. We prove polynomially effective asymptotic equidistribution results for expanding translates of $u_{\R}$-orbits and for long pieces of individual $u_{\R}$-orbits in $Γ\backslash G$. An important ingredient of the proof is the delta symbol version of the circle method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$ Strömbergsson, Andreas Södergren, Anders Vishe, Pankaj Dynamical Systems Number Theory 37A17, 37A45, 11L07 Let $G=\SL(2,\R)\ltimes(\R^2)^{k}$, let $Γ$ be a congruence subgroup of $\SL(2,\Z)\ltimes(\Z^2)^{k}$, and let $u_{\R}=(u_x)_{x\in\R}$ be the one-parameter subgroup of $G$ given by $u_x=\left(\matr 1x01,0\right)$. We prove polynomially effective asymptotic equidistribution results for expanding translates of $u_{\R}$-orbits and for long pieces of individual $u_{\R}$-orbits in $Γ\backslash G$. An important ingredient of the proof is the delta symbol version of the circle method. |
| title | Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$ |
| topic | Dynamical Systems Number Theory 37A17, 37A45, 11L07 |
| url | https://arxiv.org/abs/2604.08753 |