A regularized Siegel–Weil formula on and application to theta lifting from to

Abstract: In this paper, we obtain a second term identity of the regularized Siegel–Weil formula for the unitary dual pair , and we use this to derive a Rallis inner product formula for theta lifting from to . By choosing a good Schwartz function in the inner product formula, we obtain a special value formula for some Hecke L-function at in terms of the norm of a theta function on . [Copyright &y& Elsevier]