A Geometric Approach to Ki’s L4 Norm Bound
Trajan Hammonds (Aarhus)

The behavior of L^p norms of automorphic forms is a central topic in analytic number theory. In 2023, Haseo Ki proved the Iwaniec-Sarnak conjecture for L4 norms for Hecke-Maass cusp forms, long thought to be out of reach. In this talk, I will present joint work with Anshul Adve, along with work of Paul Nelson, providing a new proof of Haseo Ki’s optimal L4 norm bound. The key novelty is avoiding a hands-on analysis of Bessel function asymptotics, at least in the critical range. Instead we are able to recast the essential estimates into a simple problem in incidence geometry and solve it.

Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).