  The problem of summation of the perturbation series for the process of lepton
pair production in relativistic ion collisions is investigated. We show that
the amplitude of this process can be obtained in the compact analytical form,
if one confines to the terms growing as a powers of logarithm energy in the
cross section, the approximation of which is completely justified for such
colliders as RHIC and LHC. Using this result we calculate the Coulomb
corrections to the cross section of the process under consideration.
