The spin -function on for Siegel modular forms

We give a Rankin–Selberg integral representation for the Spin (degree eight) L -function on PGSp₆ that applies to the cuspidal automorphic representations associated to Siegel modular forms. If [STIX]x1D70B corresponds to a level-one Siegel modular form f of even weight, and if f has a nonvanishing maximal Fourier coefficient (defined below), then we deduce the functional equation and finiteness of poles of the completed Spin L -function [STIX]x1D6EC([STIX]x1D70B,Spin,s) of [STIX]x1D70B .