
Journal of Lie Theory 29 (2019), No. 2, 343373 Copyright Heldermann Verlag 2019 Shintani Functions for the Holomorphic Discrete Series Representation of GSp_{4}(R) Kohta Gejima Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 5600043, Japan kohta.gejima@gmail.com [Abstractpdf] 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 MuraseSugano type, which turns out to be a quotient of the $L$factors associated with $\pi$ and $\eta$. Keywords: Shintani functions, automorphic Lfunctions, zeta integrals. MSC: 11F70; 11F46, 22E50 [ Fulltextpdf (237 KB)] for subscribers only. 