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

Vishe, Pankaj (2022) 'A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$.', Transactions of the American Mathematical Society., 375 (1). pp. 669-694.

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

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1090/tran/8498
Publisher statement:First published in Transactions of the American Mathematical Society in (375:1, 2022), published by the American Mathematical Society © 2021 American Mathematical Society
Date accepted:14 June 2021
Date deposited:24 June 2021
Date of first online publication:05 November 2021
Date first made open access:24 June 2021

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