Sup-norms and fourth moment of automorphic forms

Abstract: The study of sup-norms of eigenfunctions of the Laplacian is a classical problem in harmonic analysis. In an arithmetic setting, they find further applications to L-functions and geometric questions of the underlying spaces, such as Diophantine approximation and diameters. We discuss how they have been studied in the past and how a new approach allows one to study a higher (fourth) moment. In joint work with Ilya Khayutin and Paul Nelson, we focus on the volume aspect and improve upon prior work by Templier, Harcos-Templier, Blomer-Michel, Toma.

number theory

Audience: researchers in the topic

Number theory by the sea

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