  After taking into account threshold effects, we find that the
isotropic-equivalent energies E_iso and luminosities L_iso of gamma-ray bursts
(GRBs) are correlated with redshift at the 5% and 0.9% signficance levels,
respectively. Our results are based on 10 BeppoSAX GRBs and 11 HETE-2 GRBs with
known redshifts. Our results suggest that the isotropic-equivalent energies and
luminosities of GRBs increase with redshift. They strengthen earlier clues to
this effect from analyses of the BATSE catalog of GRBs, using the variability
of burst time histories as an estimator of burst luminosities (and therefore
redshifts), and from an analysis of BeppoSAX bursts only. If the
isotropic-equivalent energies and luminosities of GRBs really do increase with
redshift, it suggests that GRB jets at high redshifts may be narrower and thus
the cores of GRB progenitor stars at high redshifts may be rotating more
rapidly. It also suggests that GRBs at very high redshifts may be more luminous
-- and therefore easier to detect -- than has been thought, which would make
GRBs a more powerful probe of cosmology and the early universe than has been
thought.
