Let G D GL2(D) where D is a quaternion division algebra over a number field F and H D Sp2(D) is the unique inner form of Sp4(F). We study the period of an automorphic form on G(A[double-struck]) relative to H(A[double-struck]) and we provide a formula, similar to the split case, for an automorphic form in the residual spectrum. We confirm the conjecture due to Dipendra Prasad for noncuspidal automorphic representations, which says that symplectic period is preserved under the global Jacquet-Langlands correspondence.
- Jacquet-Langlands correspondence
- Symplectic period
ASJC Scopus subject areas
- Mathematics (all)