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Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function Gs (z₁, z₂) for the elliptic modular group at positive integral spectral parameter s are given by logarithms of algebraic numbers in suitable class fields. We prove a partial average version of this conjecture, where we sum in the first variable z₁ over all CM points of a fixed discriminant d₁ (twisted by a genus character), and allow in the second variable the evaluation at individual CM points of discriminant d₂. This result is deduced from more general statements for automorphic Green functions on Shimura varieties associated with the group GSpin (n, 2). We also use our approach to prove a Gross–Kohnen–Zagier theorem for higher Heegner divisors on Kuga–Sato varieties over modular curves.

Mathematics Subject Classification: 11G18, 11G15, 11F37