We describe several techniques for the calculation of multi-loop
integrals and their application to heavy quark current correlators. As
new results, we present the four-loop correction to the second and third
physical moment in the low-energy expansions of vector, axial-vector and
scalar quark current correlators. Using a Ward identity, we obtain the
third and fourth moment for the pseudo-scalar correlator. We briefly
discuss the impact of these results on the determination of the charm
quark mass and the strong coupling constant using lattice simulations
for the current correlators and of the charm- and bottom-quark mass from
experimental data for σ(e+ e- → hadrons).
