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We have numerically investigated the dynamics of vortices in a clean layeredsuperconductor placed in a perpendicular magnetic field. We describe theenergetics using a Ginzburg-Landau free energy functional in the lowest Landaulevel approximation. The dynamics are determined using the time-dependentGinzburg-Landau approximation, and thermal fluctuations are incorporated via aLangevin term. The c-axis conductivity at nonzero frequencies, as calculatedfrom the Kubo formalism, shows a strong but not divergent increase as themelting temperature $T_M$ is approached from above, followed by an apparentlydiscontinuous drop at the vortex lattice freezing temperature. Thediscontinuity is consistent with the occurrence of a first-order freezing. Thecalculated equilibrium properties agree with previous Monte Carlo studies usingthe same Hamiltonian. We briefly discuss the possibility of detecting thisfluctuation conductivity experimentally.Comment: To be published in Phys. Rev.

Langevin vortex dynamics for a layered superconductor in the lowest-Landau-level approximation