Comptes Rendus
Systèmes dynamiques
Polynomial effective equidistribution
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 507-520.

Nous prouvons des théorémes d’équidistribution effectifs, avec un taux d’erreur polynomial pour les orbites des sous-groupes unipotents de SL 2 (𝔩) en quotients arithmétiques de SL 2 () et SL 2 (𝔩)×SL 2 (𝔩).

La preuve est basée sur l’utilisation d’une fonction de Margulis, des outils de la géométrie d’incidence, et le trou spectral de l’espace ambiant.

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of SL 2 (𝔩) in arithmetic quotients of SL 2 () and SL 2 (𝔩)×SL 2 (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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DOI : 10.5802/crmath.411
Elon Lindenstrauss 1 ; Amir Mohammadi 2 ; Zhiren Wang 3

1 The Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
2 Department of Mathematics, University of California, San Diego, CA 92093, USA
3 Pennsylvania State University, Department of Mathematics, University Park, PA 16802, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Elon Lindenstrauss; Amir Mohammadi; Zhiren Wang. Polynomial effective equidistribution. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 507-520. doi : 10.5802/crmath.411. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.411/

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