Peter Humphries: L^p-norm bounds for automorphic forms (NTWS 115)
Channel: Number Theory Web Seminar
Date: 2023-09-02

Abstract: A major area of study in analysis involves the distribution of mass of Laplacian eigenfunctions on a Riemannian manifold. A key result towards this is explicit L^p-norm bounds for Laplacian eigenfunctions in terms of their Laplacian eigenvalue, due to Sogge in 1988. Sogge's bounds are sharp on the sphere, but need not be sharp on other manifolds. I will discuss some aspects of this problem for the modular surface; in this setting, the Laplacian eigenfunctions are automorphic forms, and certain L^p-norms can be shown to be closely related to certain mixed moments of L-functions. This is joint with with Rizwanur Khan.

Link to slides: https://drive.google.com/file/d/1_XK8jM3hEH13CVvJZ8IuPbX2Z1d3zgYH

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, February 3, 2022 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Daylight Time, 9:30pm Indian Standard Time)
Friday, February 4, 2022 (12am CST, 3am AEDT, 5am NZDT)