Running Coupling and Borel Singularities at Small X

Starting from the dipole representation of small-x evolution we implement the running of the coupling in a self-consistent way. This results in an evolution equation for the dipole density in Borel (b) space. We show that the Borel image of the dipole density is analytic in the neighbourhood of b = 0 and that it is equal to the BFKL solution at b = 0. We study the Borel singularity structure of the dipole cascade emanating from a virtual photon at small x and nd a branch cut on the positive b-semiaxis starting at b = 1== 0. This indicates the presence of 1=Q 2 power corrections to the small-x structure functions. Finally we present numerical results in the context of D.I.S.