Shintani Functions for the Holomorphic Discrete Series Representation of GSp₄(R)

K. Gejima

Journal of Lie theory, Tome 29 (2019) no. 2, pp. 343-373

Résumé

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 $\eta$.

Détail

Classification : 11F70, 11F46, 22E50
Mots-clés : Shintani functions, automorphic L-functions, zeta integrals