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We show that the values of Borcherds products on Shimura varieties oforthogonal type at certain CM points are given in terms of coefficients of theholomorphic part of weight one harmonic weak Maass forms. Furthermore, weinvestigate the arithmetic properties of these coefficients. As an example, weobtain an analog of the Gross-Zagier theorem on singular moduli.

On CM values of Borcherds products and harmonic weak Maass forms of weight one