Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly

Configuration (x-)space renormalization of Euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group.