Victor Tan has a couple of papers on a regularized Siegel-Weil formula for U(2,2) and U(3). The papers I'm talking about are:

- "A Regularized Siegel-Weil Formula on U(2,2) and U(3)", Duke, 1998.
- "An Application of the Regularized Siegel-Weil Formula on Unitary Groups to a Theta Lifting Problem", Proceedings of the AMS, 1999.

One natural thing to look for after obtaining such a result is a Rallis inner product formula. Tan doesn't prove such a result in either of the two references mentioned above, though he seems to come close at the end of the second one.

Does anyone know if such a formula is written down anywhere?