  We use the replica method to study the ideal glass transition of a liquid of
identical Hard Spheres. We obtain estimates of the configurational entropy in
the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62,
and of the random close packing density, in the range 0.64--0.67, depending on
the approximation we use for the equation of state of the liquid. We also
compute the pair correlation function in the glassy states (i.e., dense
amorphous packings) and we find that the mean coordination number at random
close packing is equal to 6. All these results compare well with numerical
simulations and with other existing theories.
