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

Abstract We prove a weighted version of Selberg’s orthogonality conjecture for automorphic L-functions attached to irreducible cuspidal representations of GLm 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 GLm over ℚ cannot be factored further.