Heavy Quark Current Correlators to O(\alpha_s^2)

In this paper the three-loop polarization functions \Pi(q^2) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross section $\sigma (e^{+}{e}^{-}\to Z\to hadrons)$ and to the Higgs decay rates, respectively.