  Using data from equilibrium Molecular Dynamics computer simulations we have
built up a catalogue of response functions for the Coulomb one-component plasma
(OCP) over a wide range of $\Gamma$ coupling values, including the strongly
coupled $\Gamma > 1$ liquid regime. We focus on the domain of negative
compressibility ($\Gamma>3$), where causality and the concomitant
Kramers-Kronig relations are violated. We give a description of the details of
the violation, both in the frequency and time domains. We show that the
viscoelastic pole of the density response function morphs into an imaginary
pole in the upper $\omega$ half-plane that is responsible for the anomalous
behavior of the response in this coupling range. By examining the plasmon
dispersion relation through the dielectric response function, rather than via
the peaks of the dynamical structure function, we obtain a more reliable
representation for the dispersion. We demonstrate that there is an intimate
link between the formation of the roton minimum in the dispersion and the
negative compressibility of the system. The feasibility of the extension of our
analysis to systems with a short range interaction is explored.
