Theta correspondence and simple factors in global Arthur parameters. (English) Zbl 07835953
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.
Using \(L\)-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.
Using \(L\)-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.
Reviewer: Ivan Matić (Osijek)
MSC:
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 11F27 | Theta series; Weil representation; theta correspondences |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
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