Determination of a GL3 cuspform by twists of central L-values

Abstract

Let π be a self-contragredient cuspidal automorphic representations of GL3(AQ). We show that if the symmetric square L-function of π has a pole at s = 1, then π is determined by central values of quadratic twists of its L-function. That is, if π′ is another cuspidal automorphic representations of GL3(AQ) for which L( 1 2 , π⊗χ) = L( 1 2 , π′⊗χ) for sufficiently many quadratic characters χ, then π ' π′.