Polynomial effective equidistribution

Elon Lindenstrauss; Amir Mohammadi; Zhiren Wang

doi:10.5802/crmath.411

Dynamical systems

Polynomial effective equidistribution

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

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 507-520.

Abstract
Résumé

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of ${SL}_{2} (𝔩)$ in arithmetic quotients of ${SL}_{2} (ℂ)$ and ${SL}_{2} (𝔩) \times {SL}_{2} (𝔩)$ .

The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

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 ${SL}_{2} (ℂ)$ et ${SL}_{2} (𝔩) \times {SL}_{2} (𝔩)$ .

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.

Received: 2022-04-13
Revised: 2022-07-27
Accepted: 2022-08-01
Published online: 2023-02-01

DOI: 10.5802/crmath.411

Author's affiliations:

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Polynomial effective equidistribution},
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     language = {en},
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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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