The purpose of this paper is to prove the long awaited holomorphy of the third symmetric power L-functions attached to nonmonomial cusp forms of GL2 over an arbitrary number field on the whole complex plane. To be more precise, let F be a number field whose ring of adeles is A = AF . Let π = ⊗v πv be a cuspidal (unitary) representation of GL2(A). Let S be a… (More)