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.
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.
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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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