The Gross-Kohnen-Zagier theorem in higher dimensions. 
1 Oct and 31 Dec 1997, 4 March 2000. 

Duke Math. J. 97 (1999), no. 2, 219-233. 

Richard E. Borcherds, 
D.P.M.M.S., 16 Mill Lane, Cambridge, CB2 1SB, England. 
www home page www.dpmms.cam.ac.uk/~reb 

1.  Introduction. 

The Gross-Kohnen-Zagier theorem [G-K-Z] says roughly that the Heegner 
divisors of a modular elliptic curve are given by coefficients of a vector 
valued modular form of weight 3/2. We will give another proof of this (see 
theorem 4.5 and example 5.1), which extends to some more general quotients 
of hermitian symmetric spaces of dimensions b^- and shows that formal power 
series whose coefficients are higher dimensional generalizations of Heegner 
divisors are vector valued modular forms of weight 1+b^-/2.