application to the arithmetic theta correspondence, which is
modeled on , we need Howe’s abstract formulation. The additional facts we need, some
of which are special to this particular dual pair, can be found in .
2This follows from invariance under HB(Af ) of the hermitian form on MW(MB) de-
termined by the Néron-Tatepairing.
CENTRAL DERIVATIVES OF L-FUNCTIONS 355
where δp(σp, ψ−p ) is the local dichotomy sign defined in (8.2.8). Note that
the occurrence here of the additive ψ−p , where ψ
p (x) = ψp(−x), is ex-
plained in Corollary 8.2.6. Since B is indefinite