We estimate a gamma-ray burst (GRB) formation rate based on the new relation between the spectral peak energy (Ep) and the peak luminosity. The new relation is derived by combining the data of Ep and the peak luminosities by BeppoSAX and BATSE, and it looks considerably tighter and more reliable than the relations suggested by the previous works. Using the new Ep-luminosity relation, we estimate redshifts of the 689 GRBs without known distances in the BATSE catalog and derive a GRB formation rate as a function of the redshift. For the redshift range of 0 ≤ z ≤ 2, the GRB formation rate increases and is well correlated with the star formation rate, while it keeps constant toward z ∼ 12. We also discuss the luminosity function and the redshift dependence of the intrinsic luminosity (luminosity evolution).
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