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application to the arithmetic theta correspondence, which is modeled on [6], 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 [10]. 2This follows from invariance under HB(Af ) of the hermitian form on MW(MB) de- termined by the Néron-Tate pairing. 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