On the Correlation of Low-energy Spectral Indices and Redshifts of   Gamma-ray Bursts
  It was found by Amati et al. in 2002 that for a small sample of 9 gamma-ray bursts, more distant events appear to be systematically harder in the soft gamma-ray band. Here, we have collected a larger sample of 65 gamma-ray bursts, whose time integrated spectra are well established and can be well fitted with the so called Band function. It is confirmed that a correlation between the redshifts ($z$) and the low-energy indices ($\alpha$) of the Band function does exist, though it is a bit more scattered than the result of Amati et al. This correlation can not be simply attributed to the effect of photon reddening. Furthermore, correlations between $\alpha$ and $E_{\rm peak}$ (the peak energy in the $\nu F_{\nu}$ spectrum in the rest frame), $\alpha$ and $E_{\rm iso}$ (the isotropic energy release), $\alpha$ and $L_{\rm iso}$ (the isotropic luminosity) are also found, which indicate that these parameters are somehow connected. The results may give useful constraints on the physics of gamma-ray bursts. 
J. J. Geng, Y. F. Huang
astro-ph.HE