Euler products associated to metaplectic automorphic forms on the 3-fold cover of 𝐺𝑆𝑝(4)

Goetze, Thomas

doi:10.1090/S0002-9947-98-01817-0

Euler products associated to metaplectic automorphic forms on the 3-fold cover of $\mathrm {GSp}(4)$
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Trans. Amer. Math. Soc. 350 (1998), 975-1011 Request permission

Abstract:

If $\phi$ is a generic cubic metaplectic form on GSp(4), that is also an eigenfunction for all the Hecke operators, then corresponding to $\phi$ is an Euler product of degree 4 that has a functional equation and meromorphic continuation to the whole complex plane. This correspondence is obtained by convolving $\phi$ with the cubic $\theta$-function on GL(3) in a Shimura type Rankin-Selberg integral.

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