Abstract
Mathematical, particularly, asymptotic properties of the RPA and RPA with dynamic local field corrections of the coupled plasma dielectric function are analyzed within the method of moments which satisfies some exact relations. Particularly f-sum rule,higher-order sum rules and other conservation laws. Thehigher-order sum rules take into account the correlations in the system under scrutiny, so if the system dynamic characteristics, e.g., the dielectric function, do not satisfy these rules which are effectively additional conservation laws, it is difficultto expect the corresponding model to be adequate in the strong-coupling domain.Some other drawbacks and advantages of the above models are pointed out.