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We present some applications of the Kudla-Millson and the Millson theta lift.The two lifts map weakly holomorphic modular functions to vector valuedharmonic Maass forms of weight $3/2$ and $1/2$, respectively. We give finitealgebraic formulas for the coefficients of Ramanujan's mock theta functions$f(q)$ and $\omega(q)$ in terms of traces of CM-values of a weakly holomorphicmodular function. Further, we construct vector valued harmonic Maass formswhose shadows are unary theta functions, and whose holomorphic parts haverational coefficients. This yields a rationality result for the coefficients ofmock theta functions, i.e., harmonic Maass forms whose shadows lie in the spaceof unary theta functions. Moreover, the harmonic Maass forms we construct canbe used to evaluate the Petersson inner products of unary theta functions withharmonic Maass forms, giving formulas and rationality results for the Weylvectors of Borcherds products.

Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products