2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/211353We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3--loop level in renormalizable gauge field theories. These are weight {\sf w=6} harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3--loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3--loop anomalous dimensions.6 pages, to appear in the Proceedings "Loops and Legs in Quantum Field Theory 2008", Sondershausen, GermanyMathematical PhysicsHigh Energy Physics - PhenomenologyAlgebraic Geometrytext