  The cross section for ultra-high energy neutrino-nucleon scattering is very
sensitive to the parton distributions at very small values of Bjorken x ($x
\leq 10^{-4})$. We numerically investigate the effects of modifying the
behavior of the gluon distribution function at very small $x$ in the DGLAP
evolution equation. We then use the Color Glass Condensate formalism to
calculate the neutrino-nucleon cross section at ultra-high energies and compare
the result with those based on modification of DGLAP evolution equation.
