Theoretical Uncertainties in the QCD Evolution of Structure Functions and their Impact on $α_s(M_Z^2)$

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 $α_s$ from scaling violations in deep--inelastic scattering are estimated for the kinematic regime accessible at HERA.

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