Equidistribution of Fourier coefficients of integral weight Maass-Poincaré series

Abstract

We prove that the normalized Fourier coefficients of a generic family of Maass-Poincaré series of integral weight k and prime level p become quantitatively equidistributed with respect to the Sato-Tate measure as p→∞. As a consequence, we deduce similar results for harmonic Maass forms of integral weight k≤0 and level p, and weakly holomorphic modular forms of integral weight k≥2 and level p.