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

Vishe, Pankaj

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: Jun 24, 2021
• 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
• Public URL: https://durham-repository.worktribe.com/output/1273716