On the degree five $L$-function for $\mathrm {GSp}(4)$

Abstract

I give a new integral representation for the degree five (standard) L-function for automorphic representations of GSp(4) that is a refinement of integral representation of Piatetski-Shapiro and Rallis. The new integral representation unfolds to produce the Bessel model for GSp (4) which is a unique model. The local unramified calculation uses an explicit formula for the Bessel model and differs completely from Piatetski-Shapiro and Rallis.