  We present in this work new pulsational calculations for improved
carbon-oxygen DA white dwarf models suitable for the study of massive ZZ Ceti
stars. The background models employed in this study, presented in detail in a
recent paper by Althaus et al. (2003), are the result of the complete evolution
of massive white dwarf progenitors from the zero-age main sequence through the
Asymptotic Giant Branch (AGB) and mass loss phases to the white dwarf regime.
Abundance changes are accounted for by means of a full coupling between nuclear
evolution and time-dependent mixing due to convection, salt fingers, and
diffusive overshoot. In addition, time-dependent element diffusion for
multicomponent gases has been considered during the white dwarf evolution.
Crystallization and chemical rehomogenization due to phase separation upon
crystallization in the core of our models have been fully considered. The
effects of crystallization on the period spectrum of these massive white dwarf
models are assessed by means of a detailed pulsational analysis. We find that
the theoretical pulsation spectrum is strongly modified when crystallization is
considered, in particular concerning the mode trapping properties of the
equilibrium models. We also discuss at some length the implications of our
study for BPM 37093, the most massive ZZ Ceti star presently known. We find
that if BPM 37093 has a stellar mass of $\approx 1.00$ \msun its observed
spectrum could bear the signature of overshoot episodes during the helium core
burning.
