A Density Theorem for $\mathrm{Sp}(4)$

Abstract

Strong bounds are obtained for the number of automorphic forms for the group ${\Gamma }_0(q)\subseteq \mathrm{Sp}(4,\mathbb{Z})$ violating the Ramanujan conjecture at any given unramified place, which go beyond Sarnak's density hypothesis. The proof is based on a relative trace formula of Kuznetsov type, and best-possible bounds for certain Kloosterman sums for $\mathrm{Sp}(4)$.

21 pages

References in corpus (1)

• Upper bounds on L-functions at the edge of the critical strip