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 all leading logarithms of x. This gives a leading twist evolution equation for parton distributions which sums all leading logarithms of x and Q2, allowing stable perturbative evolution down to arbitrarily small values of x. Perturbative evolution then generates the double scaling rise of F2 observed at HERA, while in the formal limit x → 0 at fixed Q2 the Lipatov xf-λ behaviour is eventually reproduced. We are thus able to explain why leading order perturbation theory works so well in the HERA region.