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GRB Formation Rates inferred from the Spectral Peak Energy - Luminosity Relation

We investigate the GRB formation rate based on the relation between the spectral peak energy ($E_{p}$) and the isotropic luminosity. The $E_{p}$--luminosity relation covers the energy range of 50 -- 2000 keV and the luminosity range of $10^{50}$--$10^{54} erg/s, respectively. We find that the relation is considerably tighter than similar relations suggested previously. Using $E_{p}$--luminosity relation, we estimate the luminosity and the redshift of 684 GRBs with the unknown distances and derive the GRB formation rate as a function of the redshift. For $0 \le z \le 2$, the GRB formation rate is well correlated with the star formation rate while it increases monotonously from $z\sim 2$ out to $z \sim 12$. This behavior is consistent with the results of previous works using the lag--luminosity relation or the variability--luminosity relation.