A regularized Siegel-Weil formula on U(2,2) and U(3)

A regularized Siegel-Weil formula for unitary groups

“…We will follow [4] and compare the Fourier coefficients of maximal rank using the result of Ikeda [5] on Fourier-Jacobi coefficients. In particular, we can calculate the constant of proportionality and refine the result of Tan [26] on a regularized Siegel-Weil formula for U (2,2) and U (3). Now we will give a more precise description of our results.…”

On the Siegel–Weil formula for unitary groups

“…In [11], they introduced a regularization of the divergent theta integral, and proved an identity between a residue of the Eisenstein series and the regularized theta integral. Their regularized Siegel-Weil formula was refined by Ikeda [6], Ichino [4], and was extended to the case of unitary groups by Tan [18], Murase and Sugano [16], Ichino [5]. In this paper, following Kudla and Rallis [9], we extend the Siegel-Weil formula for unitary groups.…”

An application of the regularized Siegel-Weil formula on unitary groups to a theta lifting problem

“…Details of this formula can be found in [Tan2]. As is mentioned in the introduction, the regularized Siegel-Weil formula was first formulated (the so-called first term identity) by S. Kudla and S. Rallis in [KR] for the dual pair Sp(n) × O(m).…”

“…We may now summarize some of the main results in [Tan2]: (i) ImA −1 ∼ = Π(V 00 ) where V 00 runs over all one dimensional skew Hermitian spaces;…”

“…In this paper, we will apply a regularized Siegel-Weil formula [Tan2] to a theta lifting problem for the dual pair of unitary groups U (2) and U (2, 1) defined over a global field F . The motivation of this work come from [KR] and [KRS] which proved the regularized Siegel-Weil formula for the symplectic-orthogonal dual pair Sp(n), O(m) and applied it to poles and values of L-functions of Sp(n).…”