  We present some applications of the Kudla-Millson and the Millson theta lift.
The two lifts map weakly holomorphic modular functions to vector valued
harmonic Maass forms of weight $3/2$ and $1/2$, respectively. We give finite
algebraic 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 holomorphic
modular function. Further, we construct vector valued harmonic Maass forms
whose shadows are unary theta functions, and whose holomorphic parts have
rational coefficients. This yields a rationality result for the coefficients of
mock theta functions, i.e., harmonic Maass forms whose shadows lie in the space
of unary theta functions. Moreover, the harmonic Maass forms we construct can
be used to evaluate the Petersson inner products of unary theta functions with
harmonic Maass forms, giving formulas and rationality results for the Weyl
vectors of Borcherds products.
