On the Rankin-Selberg integral of Kohnen and Skoruppa

TL;DR

This paper extends the Rankin-Selberg integral of Kohnen and Skoruppa to a broader class of automorphic representations of PGSp_4, providing new insights into the associated Spin L-function.

Contribution

It reinterprets and generalizes the integral to arbitrary cuspidal automorphic representations of PGSp_4, connecting it to non-unique models and analyzing it with Piatetski-Shapiro and Rallis methods.

Findings

Extended the integral to all cuspidal automorphic representations of PGSp_4

Linked the integral to a non-unique model

Analyzed the integral using Piatetski-Shapiro and Rallis approach

Abstract

The Rankin-Selberg integral of Kohnen and Skoruppa produces the Spin $L$-function for holomorphic Siegel modular forms of genus two. In this paper, we reinterpret and extend their integral to apply to arbitrary cuspidal automorphic representations of $\mathrm{PGSp}_4$. We show that the integral is related to a non-unique model and analyze it using the approach of Piatetski-Shapiro and Rallis.