Journal of Lie Theory

no. 2
Shintani Functions for the Holomorphic Discrete Series Representation of GSp4(R)
Journal of Lie Theory, Volume 29 (2019) no. 2, pp. 343-373
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 $\eta$.
DOI: 10.5802/jolt.1062
Classification: 11F70, 11F46, 22E50
Keywords: Shintani functions, automorphic L-functions, zeta integrals 
@article{JOLT_2019_29_2_a2,
     author = {K. Gejima},
     title = {Shintani {Functions} for the {Holomorphic} {Discrete} {Series} {Representation} of {GSp\protect\textsubscript{4}(R)}},
     journal = {Journal of Lie Theory},
     pages = {343--373},
     year = {2019},
     volume = {29},
     number = {2},
     doi = {10.5802/jolt.1062},
     zbl = {1456.11089},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1062/}
}
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K. Gejima. Shintani Functions for the Holomorphic Discrete Series Representation of GSp4(R). Journal of Lie Theory, Volume 29 (2019) no. 2, pp. 343-373. doi: 10.5802/jolt.1062

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