Integral representation for L-functions for GSp(4) x GL(2), II

TL;DR

This paper develops an integral representation for the L-function associated with GSp(4) and GL(2) automorphic forms, enabling the proof of special value results aligned with Deligne's conjecture.

Contribution

It introduces a new integral representation for L(s,π×τ) based on Furusawa's theory, applicable to a broad class of automorphic representations.

Findings

Established an integral representation for L(s,π×τ)

Proved a special value result consistent with Deligne's conjecture

Extended Furusawa's theory to new cases involving GSp(4) and GL(2)

Abstract

Based on Furusawa's theory, we present an integral representation for the L-function L(s,\pi \times \tau), where \pi is a cuspidal automorphic representation on GSp(4) related to a holomorphic Siegel modular form, and where \tau is an arbitrary cuspidal automorphic representation on GL(2). As an application, a special value result for this L-function in the spirit of Deligne's conjecture is proved.