The asymptotic distribution of traces of Maass–Poincaré series

We establish an asymptotic formula with a power savings in the error term for traces of CM values of a family of Maass–Poincaré series which contains the modular j-function as a special case. By work of Borcherds (1998) [2], , Zagier (2002) [31], , and Bringmann and Ono (2007) [4], these traces are Fourier coefficients of half-integral weight weakly holomorphic modular forms and Maass forms.