Shintani Functions for the Holomorphic Discrete Series Representation of GSp4(R)
Journal of Lie Theory, Tome 29 (2019) no. 2, pp. 343-373
Voir la notice de l'article provenant de la source Heldermann Verlag
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 $\eta$.
Classification :
11F70, 11F46, 22E50
Mots-clés : Shintani functions, automorphic L-functions, zeta integrals
Mots-clés : Shintani functions, automorphic L-functions, zeta integrals
Affiliations des auteurs :
Kohta Gejima 1
Kohta Gejima. Shintani Functions for the Holomorphic Discrete Series Representation of GSp4(R). Journal of Lie Theory, Tome 29 (2019) no. 2, pp. 343-373. http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a2/
@article{JOLT_2019_29_2_a2,
author = {Kohta 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a2/}
}