Real Quadratic Borcherds Products

Rigid meromorphic cocycles were introduced in [DV21] to formulate a notion of singular moduli for real quadratic fields. The present work further develops their foundations and fleshes out their analogy with meromorphic modular functions with CM divisor by describing a real quadratic analogue of the Borcherds lift mapping certain weakly holomorphic modular forms of weight 1/2 to the group of rigid meromorphic cocycles with rational RM divisor.