We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of in arithmetic quotients of and .
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 en quotients arithmétiques de et .
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.
Revised:
Accepted:
Published online:
Elon Lindenstrauss 1; Amir Mohammadi 2; Zhiren Wang 3
@article{CRMATH_2023__361_G2_507_0, author = {Elon Lindenstrauss and Amir Mohammadi and Zhiren Wang}, title = {Polynomial effective equidistribution}, journal = {Comptes Rendus. Math\'ematique}, pages = {507--520}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.411}, language = {en}, }
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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