Theta correspondence and simple factors in global Arthur parameters (Q6490225)

Let \(\pi\) stand for cuspidal automorphic representation of either classical or metaplectic group over a number field \(F\). Let \(\chi\) denote a conjugate self-dual automorphic character, and let \(b\) stand for an integer.NEWLINENEWLINEUsing \(L\)-function methods, enhanced with methods of the theta correspondence, the author obtains a bound on \(b\) such that the global \(A\)-parameter of \(\pi\) has \((\chi, b)\)-factor. An implication on the global \(A\)-packets is also obtained, together with a more precise relation for \(\pi\) in a generic global \(A\)-packet.