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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1778-3569 |