Decomposition of the Coulomb electron- electron interaction into a long-range and a short-range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high-density limit for the long-range and the short-range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long-range-only electron- electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples.