#### Vol. 296, No. 2, 2018

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Zeta integrals for GSp(4) via Bessel models

### Ralf Schmidt and Long Tran

Vol. 296 (2018), No. 2, 437–480
##### 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
Primary: 11F70
##### Milestones
Received: 22 February 2017
Revised: 25 January 2018
Accepted: 18 March 2018
Published: 16 July 2018
##### Authors
 Ralf Schmidt Department of Mathematics University of Oklahoma Norman, OK 73019-3103 United States Long Tran Department of Mathematics University of Oklahoma Norman, OK 73019-3103 United States