This is a joint work with Jan Bruinier, and is a generalization of the well-known work of Gross and Zagier on singular moduli [GZ]. Here is the main result. For detail, please see [BY]. Let p ≡ 1 (mod 4) be a prime number and F = Q(√p). We write OF for the ring of integers of F , and x 7→ x′ for the conjugation in F . Let Γ = SL2(OF ) be the Hilbert modular group associated to F . The corresponding Hilbert modular surface X = Γ\H2 is a normal quasi-projective algebraic variety defined over Q. Let K = F ( √ ∆) be a non-biquadratic quartic CM number field (containing F ) with discriminant dK = p q for some prime q ≡ 1 mod 4 (technical condition). Let σ and σ′ be the complex embeddings of K given by σ( √ ∆) = σ( √ ∆′), and σ( √ ∆) = −√∆′. Then Φ = {1, σ} and Φ′ = {1, σ′} are two CM types. Let CM(K, Φ) be the (formal) sum of CM points in X of CM type (K, Φ) by OK . Then CM(K) = CM(K, Φ)+CM(K, Φ′) is an 0-cycle on X defined over Q. If Ψ is a rational modular function on X, then Ψ(CM(K)) is a rational number. An interesting and in general very hard question is to find a factorization formula for this number. We did it successfully when Ψ is a Borcherds product or equivalently has its divisor supported on the Hirzebruch-Zagier divisors, which were constructed in their seminar work in 1970’s [HZ]. Let K be the reflex field of (K, Φ) with real quadratic subfield F . For a nonzero element t ∈ d−1 K/F (relative discriminant) and a prime ideal l of F , we define