Zeta integrals for GSp(4) via Bessel models

Ralf Schmidt and Long Tran

Vol. 296 (2018), No. 2, 437–480

DOI: 10.2140/pjm.2018.296.437

Abstract

We give a revised treatment of Piatetski-Shapiro’s theory of zeta integrals and $L$-factors for irreducible, admissible representations of $GSp\left(4,F\right)$ via Bessel models. We explicitly calculate the local $L$-factors in the nonsplit case for all representations. In particular, we introduce the new concept of Jacquet–Waldspurger modules which play a crucial role in our calculations.

Keywords

L-factors, GSp(4), Bessel models, Jacquet–Waldspurger modules

Mathematical Subject Classification 2010

Primary: 11F70

Milestones

Received: 22 February 2017

Revised: 25 January 2018

Accepted: 18 March 2018

Published: 16 July 2018