Siu Hang Man (University of Bonn): A density theorem for $Sp(4)$

Abstract: We prove a density theorem that bounds the number of automorphic forms of level $q$ for the group $Sp(4)$ that violates the Ramanujan conjecture relative to the amount by which they violate the conjecture, which goes beyond Sarnak’s density hypothesis. The proof relies on a relative trace formula of Kuznetsov type, and non-trivial bounds for certain $Sp(4)$ Kloosterman sums.

The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.