Improved Generalized Periods Estimates Over Curves on Riemannian Surfaces with Nonpositive Curvature

Emmett L. Wyman, Yakun Xi

We show that on compact Riemann surfaces of nonpositive curvature, the generalized periods, i.e. the $\nu$-th order Fourier coefficients of eigenfunctions $e_{\lambda }$ over a closed smooth…