Langlands–Shahidi method and poles of automorphic L-functions III: Exceptional groups

In this paper, we apply Langlands–Shahidi method to exceptional groups, with the assumption that the cuspidal representations have one spherical tempered component. A basic idea is to use the fact that the local components of residual automorphic representations are unitary representations, and use the classification of the unitary dual. We prove non-unitarity of certain spherical representations of exceptional groups. We need to divide into five different cases, and in two cases we can prove that the completed L-functions are holomorphic except possibly at 0, 1/2, 1 under some local assumptions.