Polynomial effective equidistribution
We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\mathrm{SL}_2(\mathfrak{l})$ in arithmetic quotients of $\mathrm{SL}_2(\mathbb{C})$ and $\mathrm{SL}_2(\mathfrak{l})\times \mathrm{SL}_2(\mathfrak{l})$.The proof is based on the use of...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-02-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.411/ |
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| author | Lindenstrauss, Elon Mohammadi, Amir Wang, Zhiren |
| author_facet | Lindenstrauss, Elon Mohammadi, Amir Wang, Zhiren |
| author_sort | Lindenstrauss, Elon |
| collection | DOAJ |
| description | We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\mathrm{SL}_2(\mathfrak{l})$ in arithmetic quotients of $\mathrm{SL}_2(\mathbb{C})$ and $\mathrm{SL}_2(\mathfrak{l})\times \mathrm{SL}_2(\mathfrak{l})$.The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space. |
| format | Article |
| id | doaj-art-20061efc74ab494b8a96dfae2809a9e1 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-20061efc74ab494b8a96dfae2809a9e12025-02-07T11:06:36ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-02-01361G250752010.5802/crmath.41110.5802/crmath.411Polynomial effective equidistributionLindenstrauss, Elon0Mohammadi, Amir1Wang, Zhiren2The Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, IsraelDepartment of Mathematics, University of California, San Diego, CA 92093, USAPennsylvania State University, Department of Mathematics, University Park, PA 16802, USAWe prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\mathrm{SL}_2(\mathfrak{l})$ in arithmetic quotients of $\mathrm{SL}_2(\mathbb{C})$ and $\mathrm{SL}_2(\mathfrak{l})\times \mathrm{SL}_2(\mathfrak{l})$.The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.411/ |
| spellingShingle | Lindenstrauss, Elon Mohammadi, Amir Wang, Zhiren Polynomial effective equidistribution Comptes Rendus. Mathématique |
| title | Polynomial effective equidistribution |
| title_full | Polynomial effective equidistribution |
| title_fullStr | Polynomial effective equidistribution |
| title_full_unstemmed | Polynomial effective equidistribution |
| title_short | Polynomial effective equidistribution |
| title_sort | polynomial effective equidistribution |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.411/ |
| work_keys_str_mv | AT lindenstrausselon polynomialeffectiveequidistribution AT mohammadiamir polynomialeffectiveequidistribution AT wangzhiren polynomialeffectiveequidistribution |