Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions

We prove a weighted version of Selberg's orthogonality conjecture for automorphic L-functions attached to irreducible cuspidal representations of GL(m) over Q. Using this weighted orthogonality, we obtain the uniqueness of factorization of general L-functions. As a consequence, we prove that the L-function attached to an automorphic irreducible cuspidal representation of GL(m) over Q cannot be factored further.