Analytic Approach to Small-X Structure Functions

We present a method for the analytic solution of small $x$ structure functions. The essential small $x$ logarithms are summed to all orders in the anomalous dimensions and coefficient functions. Although we work at leading logarithmic accuracy, the method is general enough to allow the systematic inclusion of sub-leading logarithms. Results and predictions are presented for the gluon density, and the structure functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$. We find that corrections to the simple double logarithmic calculation are important in the HERA range and obtain good fits to all available data.