Uniform Bounds for Period Integrals and Sparse Equidistribution

Tanis, J.; Vishe, P.

doi:10.1093/imrn/rnv115

Uniform Bounds for Period Integrals and Sparse Equidistribution

Tanis, J.; Vishe, P.

Authors

J. Tanis

Dr Pankaj Vishe pankaj.vishe@durham.ac.uk
Associate Professor

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

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Copyright Statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in International mathematics research notices following peer review. The version of record Tanis, J. & Vishe, P. (2015). Uniform Bounds for Period Integrals and Sparse Equidistribution. International Mathematics Research Notices 2015(24): 13728-13756 is available online at: https://doi.org/10.1093/imrn/rnv115