Speakers: Trajan Hammonds (Princeton University)

Title: 𝐿⁴ Norms of Maass Forms

Abstract: In early 2023, Haseo Ki proved the optimal bound for 𝐿⁴ norms of Maass forms. That is, for Maass forms of Laplace eigenvalue 𝜆, their 𝐿⁴ norm is bounded by 𝜆 ^𝜖 . While the proof was generally understood to be correct, there was little understanding among the number theory community what was really going on. In this talk, I’ll present a much more transparent approach via Fourier analysis to recover the optimal bound in the most difficult range. This is joint work with Anshul Adve.