The completed standard L-function of modular forms on G2
Source
arXiv
Date Issued
2021-04-01
Author(s)
Cicek, Fatma
Davidoff, Giuliana
Dijols, Sarah
Hammonds, Trajan
Pollack, Aaron
Roy, Manami
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 ? is a cuspidal automorphic representation of G2(A) corresponding to a level one, even weight modular form ? on G2, we define an associated completed standard L-function, ?(?,Std,s). Assuming that a certain Fourier coefficient of ? is nonzero, we prove the functional equation ?(?,Std,s)=?(?,Std,1?s). The proof proceeds via a careful analysis of a Rankin-Selberg integral due to Gurevich and Segal.
Subjects
Number Theory
Representation Theory
