====== TTP06-23 Recent Results on Four-loop Tadpoles ====== The experimental measurable R-ratio can be used to perform a precise determination of the charm- and bottom-quark mass with the help of theoretical computable expansion coefficients of the vacuum polarization function. The four-loop contributions in perturbative QCD to the first two expansion coefficients of the vacuum polarization functions are presented. |**K.G. Chetyrkin, J.H. K\"uhn and C. Sturm** | |** Nucl. Phys. (Proc. Suppl.) B160 230-234 2006 ** | | {{preprints:2006:ttp06-23.pdf|PDF}} {{preprints:2006:ttp06-23.ps|PostScript}} | | |