Abstract
We use the hard (Lipatov) pomeron for the low-x gluon distribution and provide a compact formula for the ratio that is useful to extract the charm structure function from the reduced charm cross-section, in particular at DESY HERA. Our results show that this ratio is independent of x and independent of the DGLAP evolution of the gluon PDF. As a result, we show that the charm structure function and the reduced charm cross-section exponents do not have the same behaviour at very low x. This difference is independent of the input gluon distribution functions and predicts the non-linear effects and some evidence for shadowing and antishadowing at HERA and RHIC.
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