Functoriality for the exterior square of

In this paper we prove the functoriality of the exterior square of cusp forms on as automorphic forms on and the symmetric fourth of cusp forms on as automorphic forms on . We prove these by applying a converse theorem of Cogdell and Piatetski-Shapiro to analytic properties of certain -functions obtained by the Langlands-Shahidi method. We give several applications: First, we prove the weak Ramanujan property of cuspidal representations of and the absolute convergence of the exterior square -functions of . Second, we prove that the fourth symmetric power -functions of cuspidal representations of are entire, except for those of dihedral and tetrahedral type. Third, we prove the bound for Hecke eigenvalues of Maass forms over any number field.