Let
where
is a quaternion division algebra over a number field
and
is the unique
inner form of
.
We study the period of an automorphic form on
relative
to
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.
