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A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$

Vishe, Pankaj

A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$ Thumbnail


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Abstract

Let G = SL(2, R) n, let Γ = Γn 0 , where Γ0 is a co-compact lattice in SL(2, R), let F(x) be a non-singular quadratic form and let u(x1, ..., xn) := 1 x1 0 1 ×...× 1 xn 0 1 denote unipotent elements in G which generate an n dimensional horospherical subgroup. We prove that in the absence of any local obstructions for F, given any x0 ∈ G/Γ, the sparse subset {u(x)x0 : x ∈ Z n, F(x) = 0} equidistributes in G/Γ as long as n ≥ 481, independent of the spectral gap of Γ

Citation

Vishe, P. (2022). A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$. Transactions of the American Mathematical Society, 375(1), 669-694. https://doi.org/10.1090/tran/8498

Journal Article Type Article
Acceptance Date Jun 14, 2021
Online Publication Date Nov 5, 2021
Publication Date 2022
Deposit Date Jun 23, 2021
Publicly Available Date Mar 28, 2024
Journal Transactions of the American Mathematical Society
Print ISSN 0002-9947
Electronic ISSN 1088-6850
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 375
Issue 1
Pages 669-694
DOI https://doi.org/10.1090/tran/8498

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