Exceptional poles of local spinor $L$-functions of $\mathrm{GSp}(4)$ with anisotropic Bessel models

TL;DR

This paper identifies the exceptional poles of the spinor L-function for certain non-cuspidal representations of GSp(4) over local fields, focusing on anisotropic Bessel models, advancing understanding of local L-factors.

Contribution

It precisely determines the exceptional poles of the spinor L-function for non-cuspidal GSp(4) representations with anisotropic Bessel models, a new result in local representation theory.

Findings

Identified exceptional poles of the spinor L-function.

Connected poles to anisotropic Bessel models.

Enhanced understanding of local L-factors for GSp(4).

Abstract

For non-cuspidal irreducible admissible representations of $\mathrm{GSp}(4,k)$ over a local non-archimedean field $k$, we determine the exceptional poles of the spinor $L$-factor attached to anisotropic Bessel models by Piatetski-Shapiro.