The Regularized Siegel-Weil Formula (The Second Term Identity) and the   Rallis Inner Product Formula
  In this paper, we establish the second term identity of the Siegel-Weil formula in full generality, and derive the Rallis inner product formula for global theta lifts for any dual pair. As a corollary, we resolve the non-vanishing problem of global theta lifts initiated by Steve Rallis. 
Wee Teck Gan, Yannan Qiu and Shuichiro Takeda
math.NT math.RT