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The determination of luminosity function (LF) of gamma-ray bursts (GRBs) isof an important role for the cosmological applications of the GRBs, which ishowever hindered seriously by some selection effects due to redshiftmeasurements. In order to avoid these selection effects, we suggest tocalculate pseudo-redshifts for Swift GRBs according to the empirical L-E_prelationship. Here, such a $L-E_p$ relationship is determined by reconcilingthe distributions of pseudo- and real redshifts of redshift-known GRBs. Thevalues of E_p taken from Butler's GRB catalog are estimated with Bayesianstatistics rather than observed. Using the GRB sample with pseudo-redshifts ofa relatively large number, we fit the redshift-resolved luminositydistributions of the GRBs with a broken-power-law LF. The fitting resultssuggest that the LF could evolve with redshift by a redshift-dependent breakluminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- andhigh-luminosity indices are constrained to 0.8 and 2.0, respectively. It isfound that the proportional coefficient between GRB event rate and starformation rate should correspondingly decrease with increasing redshifts.

Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts