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We compare the leading and next-to-leading order Quantum Chromodynamics predictions for the flux of atmospheric muons and neutrinos from decays of charmed particles. We then compute this flux for different Partonic Distribution Functions (PDF's) and different extrapolations of these at small partonic momentum fraction x. We find that the predicted fluxes vary up to almost two orders of magnitude at the largest energies studied, depending on the chosen extrapolation of the PDF's. We show that the spectral index of the atmospheric leptonic fluxes depends linearly on the slope of the gluon distribution function at very small x. Finally, we analyze the uncertainties of our model and we consider the dependence of our simulation on the primary cosmic ray flux.

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