Regular poles for spinor $L$-series attached to split Bessel models of $\mathrm{GSp}(4)$

Mirko Rösner and Rainer Weissauer

Vol. 337 (2025), No. 1, 137–199

DOI: 10.2140/pjm.2025.337.137

Abstract

For irreducible smooth representations $\mathrm{\Pi }$ of $\mathrm{GSp}<!--FUNCTION\; APPLICATION-->(4,k)$ over a nonarchimedean local field $k$, Piatetski-Shapiro and Soudry (1981) have constructed an $L$-factor depending on the choice of a Bessel model. It factorizes into a regular part and an exceptional part. We determine the regular part for the case of split Bessel models.

Keywords

spinor $L$-function, symplectic groups, Bessel models

Mathematical Subject Classification 2010

Primary: 22E50

Secondary: 11F46, 11F70, 20G05

Milestones

Received: 19 December 2019

Accepted: 18 February 2025

Published: 2 June 2025