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(4,F) 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
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