A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces

Andre Reznikov

doi:https://doi.org/10.1515/forum-2012-0185

A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces

Andre Reznikov

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider periods along closed geodesics and along geodesic circles for eigenfunctions of the Laplace-Beltrami operator on a compact hyperbolic Riemann surface. We obtain uniform bounds for such periods as the corresponding eigenvalue tends to infinity. We use methods from the theory of automorphic functions and, in particular, the uniqueness of the corresponding invariant functionals on irreducible unitary representations of PGL₂(ℝ).

Original language	English
Pages (from-to)	1569-1590
Number of pages	22
Journal	Forum Mathematicum
Volume	27
Issue number	3
DOIs	https://doi.org/10.1515/forum-2012-0185
State	Published - 1 May 2015

Keywords

Eigenfunctions
Laplace operator
hyperbolic surfaces
periods

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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https://doi.org/10.1515/forum-2012-0185

Cite this

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A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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