Paul Nelson: The sup norm problem in the level aspect (NTWS 140)
Channel: Number Theory Web Seminar
Date: 2023-05-19

Abstract: The sup norm problem concerns the size of L^2-normalized eigenfunctions of manifolds.  In many situations, one expects to be able to improve upon the general bound following from local considerations.  The pioneering result in that direction is due to Iwaniec and Sarnak, who in 1995 established an improvement upon the local bound for Hecke-Maass forms of large eigenvalue on the modular surface.  Their method has since been extended and applied by many authors, notably to the "level aspect" variant of the problem, where one varies the underlying manifold rather than the eigenvalue.  Recently, Raphael Steiner introduced a new method for attacking the sup norm problem.  I will describe joint work with Raphael Steiner and Ilya Khayutin in which we apply that method to improve upon the best known bounds in the level aspect.

Link to slides: https://drive.google.com/file/d/1tzDb8vxBC_gZvo8P0mUrCHRuNH6u5fCS

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

Original air date: 
Thursday, September 29, 2022 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, September 30, 2022 (1am AEST, 4am NZDT)