The Spin $L$-function on ${\mathrm{GSp}}_6$ for Siegel modular forms

Abstract

We give a Rankin-Selberg integral representation for the Spin (degree eight) $L$-function on ${\mathrm{PGSp}}_6$. The integral applies to the cuspidal automorphic representations associated to Siegel modular forms. If $\ddot{I}€$ corresponds to a level one Siegel modular form $f$ of even weight, and if $f$ has a non-vanishing maximal Fourier coefficient (defined below), then we deduce the functional equation and finiteness of poles of the completed Spin $L$-function $\hat{I}›(\ddot{I}€,Spin,s)$ of $\ddot{I}€$.

differs slightly from published counterpart