Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.We report on the progress we made in studying the infrared behavior of the ghost and gluon
dressing functions in Landau gauge. Related to this we also investigate a running coupling given
in terms of those functions and compare our results to those coming from the Dyson-Schwinger
approach. We present first numerical results for the SU(3) ghost-ghost-gluon vertex renormalization
constant. In addition the spectrum of low-lying eigenvalues and eigenfunctions of the
Faddeev-Popov operator is determined. The saturation of the ghost propagator in terms of those
eigenvalues and eigenmodes is discussed at lower momenta
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