A Singular Theta Lift in SU(1,1)

Following the work of Bruinier and Funke in the orthogonal setting, we consider a regularised theta lift from weight 0 harmonic weak Maass forms on non-compact quotients of SU(1,1) to meromorphic modular forms of weight 2, and realise the result of the lift as a generating series of modular traces of those Maass forms on CM points. We also lift the non-holomorphic Eisenstein series of weight 0 and realise the derivative of a suitably normalised weight 2 Eisenstein series as the lift of the logarithm of the modular Delta function