On the degree five 𝐿-function for 𝐺𝑆𝑝(4)

File, Daniel

doi:10.1090/S0002-9947-2013-05869-2

On the degree five $L$-function for $\mathrm {GSp}(4)$
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Trans. Amer. Math. Soc. 365 (2013), 6471-6497 Request permission

Abstract:

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

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