Abstract:
Modular forms on the split exceptional group G2 over Q are a special class of automorphic forms on this group, which were introduced by Gan, Gross, and Savin. If π is a cuspidal automorphic representation of G2(A) corresponding to a level one, even weight modular form φ on G2, we define an associated completed standard L-function, Λ(π,Std,s). Assuming that a certain Fourier coefficient of φ is nonzero, we prove the functional equation Λ(π,Std,s)=Λ(π,Std,1−s). The proof proceeds via a careful analysis of a Rankin-Selberg integral due to Gurevich and Segal.