CM VALUES OF REGULARIZED THETA LIFTS AND HARMONIC WEAK MAASS FORMS OF WEIGHT 1

We study special values of regularized theta lifts at complex multiplication (CM) points. In particular; we show that CM values of Borcherds products can be expressed in terms of finitely many Fourier coefficients of certain harmonic weak Maafi forms of weight 1. As it turns out, these coefficients are logarithms of algebraic integers whose prime ideal factorization is determined by special cycles on an arithmetic curve. Our results imply a conjecture of Duke and Li and give a new proof of the modularity of a certain arithmetic generating series of weight 1 studied by Kudla, Rapoport, and Yang.