Аннотация:It is shown that, in the existing theory of the resonance (phononless) AC hopping conductivity, the one-particle density of states with a Coulomb gap generally cannot be used in the calculation of the resonance AC conductivity. In a wide frequency range, the correlations between the one-electron energies of the active pairs should be taken into account predicting a slightly sublinear frequency behavior of the conductivity in the entire frequency range of interest, rather than the crossover from linear to quadratic frequency dependence.