Bessel models for $GSp(4)$

TL;DR

This paper uses theta correspondence to analyze Bessel models for GSp(4), confirming a conjecture that links these models to local epsilon factors and central L-value non-vanishing.

Contribution

It proves a conjecture of Gross and Prasad relating Bessel models to epsilon factors and L-values using theta correspondence methods.

Findings

Bessel models characterized by local epsilon factors

Global non-vanishing of central L-values linked to Bessel models

Confirmation of Gross-Prasad conjecture for GSp(4)

Abstract

Methods of theta correspondence are used to analyze local and global Bessel models for $GSp(4)$ proving a conjecture of Gross and Prasad which describes these models in terms of local epsilon factors in the local case, and the non-vanishing of central critical $L$-value in the global case.