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In this paper, we establish the second term identity of the Siegel-Weilformula in full generality, and derive the Rallis inner product formula forglobal theta lifts for any dual pair. As a corollary, we resolve thenon-vanishing problem of global theta lifts initiated by Steve Rallis.

The Regularized Siegel-Weil Formula (The Second Term Identity) and the Rallis Inner Product Formula