Uniform Bounds for Period Integrals and Sparse Equidistribution

Tanis, J.; Vishe, P.

Abstract

Let M=Γ∖PSL(2,R) be a compact manifold, and let f∈C∞(M) be a function of zero average. We use spectral methods to get uniform (i.e., independent of spectral gap) bounds for twisted averages of f along long horocycle orbit segments. We apply this to obtain an equidistribution result for sparse subsets of horocycles on M.

Citation

Tanis, J., & Vishe, P. (2015). Uniform Bounds for Period Integrals and Sparse Equidistribution. International Mathematics Research Notices, 2015(24), 13728-13756. https://doi.org/10.1093/imrn/rnv115

• Journal Article Type: Article
• Acceptance Date: Mar 31, 2015
• Online Publication Date: Apr 30, 2015
• Publication Date: Apr 30, 2015
• Deposit Date: Dec 30, 2015
• Publicly Available Date: Sep 13, 2017
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 24
• Pages: 13728-13756
• DOI: https://doi.org/10.1093/imrn/rnv115
• Public URL: https://durham-repository.worktribe.com/output/1395826