Theoretical Uncertainties in the QCD Evolution of Structure Functions   and their Impact on $\alpha_s(M_Z^2)$
  The differences are discussed between various next-to-leading order prescriptions for the QCD evolution of parton densities and structure functions. Their quantitative impact is understood to an accuracy of 0.02\%. The uncertainties due to the freedom to choose the renormalization and factorization scales are studied. The quantitative consequences of the different uncertainties on the extraction of the strong coupling constant $\alpha_s$ from scaling violations in deep--inelastic scattering are estimated for the kinematic regime accessible at HERA. 
J. Bl\"umlein, S. Riemersma, W.L. van Neerven, and A. Vogt