Dr Pankaj Vishe pankaj.vishe@durham.ac.uk
Associate Professor
A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$
Vishe, Pankaj
Authors
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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Accepted Journal Article
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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Statement
First published in Transactions of the American Mathematical Society in (375:1, 2022), published by the American Mathematical Society © 2021 American Mathematical Society
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