  We have numerically investigated the dynamics of vortices in a clean layered
superconductor placed in a perpendicular magnetic field. We describe the
energetics using a Ginzburg-Landau free energy functional in the lowest Landau
level approximation. The dynamics are determined using the time-dependent
Ginzburg-Landau approximation, and thermal fluctuations are incorporated via a
Langevin term. The c-axis conductivity at nonzero frequencies, as calculated
from the Kubo formalism, shows a strong but not divergent increase as the
melting temperature $T_M$ is approached from above, followed by an apparently
discontinuous drop at the vortex lattice freezing temperature. The
discontinuity is consistent with the occurrence of a first-order freezing. The
calculated equilibrium properties agree with previous Monte Carlo studies using
the same Hamiltonian. We briefly discuss the possibility of detecting this
fluctuation conductivity experimentally.
