Integral Representaion for L-functions for GSp(4)xGL(2)

TL;DR

This paper develops an integral representation for the degree-8 L-function associated with GSp(4) and GL(2) automorphic forms, extending previous methods to include new cases such as square-free levels and Maass forms.

Contribution

It refines Furusawa's method to cover broader classes of automorphic representations and derives new special value results for the associated L-functions.

Findings

Integral representation for L(s,pi x tau) obtained

Includes cases with square-free level and Maass forms

Provides new special value results for the L-function

Abstract

Let pi be a cuspidal, automorphic representation of GSp(4) attached to a Siegel modular form of degree 2. We refine the method of Furusawa to obtain an integral representation for the degree-8 L-function L(s,pi x tau), where tau runs through certain cuspidal, automorphic representation of GL(2). Our calculations include the case of square-free level for the p-adic components of tau, and a wide class of archimedean types including Maass forms. As an application we obtain a special value result for L(s,pi x tau).