A density theorem for Sp(4) — Siu Hang Man (Charles University)

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.