The results of numerical calculations, in different approximations, of the screened Coulomb and retarded electron-plasmon interactions in quasi-two-dimensional layered crystals and two-dimensional (2D) systems with a quasi-acoustic or square-root plasmon spectrum are subjected to a detailed comparative analysis. It is shown that even in the simplest, random-phase approximation the effective attraction due to the exchange of virtual plasmons can bring about a transition to a superconducting state with a relatively high critical temperature Tc. The extended saddle-point singularities typical of the 2D band spectrum of layered crystals of cuprate metaloxide compounds and also the many-particle Coulomb correlations described by Coulomb vertices (three-poles) make for a substantial increase in the maximum values of Tc, which agree with the experimental data for high-Tc superconductors. It is shown that the plasmon mechanism leads to Cooper pairing in both the d-wave and s-wave Cooper channels, but the superconductivity in the s-wave channel is suppressed by exchange-correlation effects. Calculations also indicate the possibility of obtaining rather high-Tc superconductivity in 2D systems (of the graphene type).

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