  We present the main results of a study of spectral and energetics properties
of twelve gamma-ray bursts (GRBs) with redshift estimates. All GRBs in our
sample were detected by BeppoSAX in a broad energy range (2-700 keV). From the
redshift estimates and the good-quality BeppoSAX time-integrated spectra we
deduce the main properties of GRBs in their cosmological rest frames. All
spectra in our sample are satisfactorily represented by the Band model with no
significant soft X-ray excesses or spectral absorptions. We find a positive
correlation between the estimated total (isotropic) energies in the 1-10000 keV
energy range (E_rad) and redshifts z. Interestingly, more luminous GRBs are
characterized also by larger peak energies E_p of their EF(E) spectra.
Furthermore, more distant GRBs appear to be systematically harder in the X-ray
band compared to GRBs with lower redshifts. We discuss how selection and data
truncation effects could bias our results and give possible explanations for
the correlations that we found.
