Harmonic weak Maass forms and periods II

In this paper we investigate the Fourier coefficients of harmonic Maass forms of negative half-integral weight. We relate the algebraicity of these coefficients to the algebraicity of the coefficients of certain canonical meromorphic modular forms of positive even weight with poles at Heegner divisors. Moreover, we give an explicit formula for the coefficients of harmonic Maass forms in terms of periods of certain meromorphic modular forms with algebraic coefficients.