Integrality Properties of the Cm-values of Certain Weak Maass Forms

In a recent paper, Bruinier and Ono prove that the coefficients of certain weight −1/2 harmonic Maass forms are traces of singular moduli for weak Maass forms. In particular, for the partition function p(n), they prove that p(n) = 1 24n− 1 · ∑ Pp(αQ), where Pp is a weak Maass form and αQ ranges over a finite set of discriminant −24n + 1 CM points. Moreover, they show that 6 · (24n − 1) · Pp(αQ) is always an algebraic integer, and they conjecture that (24n − 1) · Pp(αQ) is always an algebraic integer. Here we prove a general theorem which implies this conjecture as a corollary.