Quantum corrections to the Weizsacker-Williams gluon distribution function at small x

We compute the quantum corrections to the gluon distribution function in the background of a non-Abelian Weizsacker-Williams field. These corrections are valid to all orders in the effective coupling alpha(s) mu, where mu(2) denotes the average valence quark color charge squared per unit area. We find ln(1/x) logarithmic corrections to the classical gluon distribution function. The one-loop corrections to the classical Weizsacker-Williams field do not contribute to these singular terms in the distribution function. Their effect is to cause the running of alpha(s).