SUMMATION OF LEADING LOGARITHMS AT SMALL-X

We show how perturbation theory may be reorganized to give splitting functions which include order by order convergent sums of al leading logarithms of x. This gives a leading twist evolution equation for parton distributions which sums all leading logarithms of x and Q(2), allowing stable perturbative evolution down to arbitrarily small values of x. Perturbative evolution then generates the double scaling rise of F-2 observed at HERA, while in the formal limit x --> 0 at fixed Q(2) the Lipatov x(-lambda) behaviour is eventually reproduced. We are thus able to explain why leading order perturbation theory works so well in the HERA region.