Journal of Lie Theory 29 (2019), No. 2, 343--373
Copyright Heldermann Verlag 2019
Shintani Functions for the Holomorphic Discrete Series Representation of GSp4(R)
Kohta Gejima
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
kohta.gejima@gmail.com
[Abstract-pdf]
Let $\pi$ be the holomorphic discrete series representation of $GSp_4(\mathbb{R})$ and $\eta$ the discrete series representation of $(GL_2 \times_{GL_1} GL_2)(\mathbb{R})$. We prove the uniqueness and an explicit formula of the Shintani functions for $(\pi,\eta)$. As their application, we evaluate a local zeta integral of Murase-Sugano type, which turns out to be a quotient of the $L$-factors associated with $\pi$ and $\eta$.
Keywords: Shintani functions, automorphic L-functions, zeta integrals.
MSC: 11F70; 11F46, 22E50
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