Symplectic Kloosterman Sums and Poincaré Series

Abstract

We prove power-saving bounds for general Kloosterman sums on $\mathrm{Sp}(4)$ associated to all Weyl elements via a stratification argument coupled with $p$-adic stationary phase methods. We relate these Kloosterman sums to the Fourier coefficients of $\mathrm{Sp}(4)$ Poincaré series.

Published version

References in corpus (2)

• An orthogonality relation for GL(4,R)
• On Estimates of Exponential Sums