Let be an arithmetic hyperbolic surface arising from a quaternion division algebra over . Let be a Hecke–Maass form on , and let be a geodesic segment. We obtain a power saving over the local bound of Burq, Gérard, and Tzvetkov for the -norm of restricted to , by extending the technique of arithmetic amplification developed by Iwaniec and Sarnak. We also improve the local bounds for various Fourier coefficients of along .
"Geodesic restrictions of arithmetic eigenfunctions." Duke Math. J. 165 (3) 463 - 508, 15 February 2016. https://doi.org/10.1215/00127094-3166736