# Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature

@article{Wyman2021ImprovedGP,
title={Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature},
author={Emmett L. Wyman and Yakun Xi},
journal={Forum Mathematicum},
year={2021},
volume={33},
pages={789 - 807}
}
• Published 29 June 2018
• Mathematics
• Forum Mathematicum
Abstract We show that, on compact Riemannian surfaces of nonpositive curvature, the generalized periods, i.e. the 𝜈-th order Fourier coefficients of eigenfunctions eλe_{\lambda} over a closed smooth curve 𝛾 which satisfies a natural curvature condition, go to 0 at the rate of O⁢((log⁡λ)-12)O((\log\lambda)^{-\frac{1}{2}}) in the high energy limit λ→∞\lambda\to\infty if 0<|ν|λ<1-δ0<\frac{\lvert\nu\rvert}{\lambda}<1-\delta for any fixed 0<δ<10<\delta<1. Our result implies, for instance, that the… Expand
2 Citations

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