The singularities of the fluctuations of the density and electric field in a nondegenerate ideal electron gas are discussed. Classical calculations for a point electron lead to an infinity in the spectral energy distribution of the Coulomb field. Measurements of the spectral energy distribution in the classical frequency region and the elimination of the singularity by incorporating quantum fluctuations are discussed. The space-time correlation function of the density fluctuations in a nondegenerate ideal gas is discussed.