Abstract
In this paper, we first review and summarize some recent progress in Kudla program on unitary Shimura varieties. We show how the local arithmetic Siegel-Weil formula implies the global arithmetic Siegel-Weil formula for non-singular coefficients on $\rU(n,1)$. In particular, the arithmetic Siegel-Weil formula for non-singular coefficients on $\rU(1,~1)$ is true.
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