Abstract
Next-to-leading order corrections to jet cross sections in deep inelastic scattering at HERA are studied. The predicted jet rates allow for a precise determination of $\alpha_s(\mu_R)$ at HERA over a wide range of $\mu_R$. We argue, that the ``natural'' renormalization and factorization scale is set by the average $k_T^B$ of the jets in the Breit frame and suggest to divide the data in corresponding $<k_T^B>$ intervals. Some implications for the determination of the gluon density and the associated forward jet production in the low $x$ regime at HERA are briefly discussed.
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