THE EVOLUTION OF PARTON DISTRIBUTIONS AT SMALL-X

We investigate parton distributions at small x using moments of the Gr ibov-Lipatov-Altarelli-Parisi (GLAP) evolution equation with respect t o x. In this representation the kernel of the GLAP equation contains s ingularities in the moment variable omega at omega = 0. We show that t he importance of these singularities at small x depends on the form of the starting distributions. We examine the range of x in which the GL AP equation is valid. The restrictions on the range of x depend on the form of the starting distributions. We investigate whether the GLAP e quation can be used to interpolate data in the HERA region. Results ar e given for the structure function F2 at small x. A possible method of determining the gluon distribution from F2 is discussed.