Equidistribution of continuous low-lying pairs of horocycles via Ratner’s theorem

Claire Burrin

doi:10.5802/crmath.693

Research article - Dynamical systems

Equidistribution of continuous low-lying pairs of horocycles via Ratner’s theorem

Claire Burrin ¹

¹ Institute of Mathematics, University of Zurich, Switzerland

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1-5

Abstract (Original language)
Résumé

We record an alternative proof of a recent joint equidistribution result of Blomer and Michel, based on Ratner’s topological rigidity theorem. This approach has the advantage of extending to non-uniform lattices.

Nous présentons une preuve alternative d’un résultat récent d’équidistribution jointe de Blomer et Michel, basée sur le théorème de rigidité topologique de Ratner. Cette approche a l’avantage de s’étendre aux réseaux non uniformes.

Received: 2024-08-01
Revised: 2024-09-23
Accepted: 2024-09-28
Published online: 2025-03-06

DOI: 10.5802/crmath.693

Classification: 37A10, 37A44, 22F30
Keywords: Joint equidistribution, measure classification, commensurator, Hecke operators, matrix coefficients
Mots-clés : Équidistribution jointe, classification des mesures, commensurateur, opérateurs de Hecke, coefficients matriciels

Author's affiliations:

Claire Burrin ¹

¹ Institute of Mathematics, University of Zurich, Switzerland

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Claire Burrin. Equidistribution of continuous low-lying pairs of horocycles via Ratner’s theorem. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1-5. doi: 10.5802/crmath.693

References
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