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中文摘要：
伽玛射线暴的产生机制比较公认的是：长暴产生于大质量恒星死亡；短暴产生于密近双星合并．因此人们很自然地推测长暴和恒星形成率直接成比例，但是最近数据分析表明这并不能很好地拟合观测．考虑到只有质量大于某一临界质量的大质量恒星才可能产生长暴，因此恒星初始质量分布函数对长暴的产生率会有较大影响．考虑用恒星初始质量分布函数来解释长暴观测个数随红移的分布，得到了比较好的结果．
英文摘要：
It has been recognized that the long duration gamma-ray bursts（LGRBs） originate from core collapsing of massive stars and the short duration gamma-ray bursts（SGRBs） originate from merging of tight binary systems. So it is naturally speculated that the LGRBs should follow the star formation rate （SFR）, but the recent calculation indicated that the LGRB did not exactly trace the SFR . Since only massive star can produce LGRB, the initial mass function （IMF） should have significant influence on the GRB rate . Here we calculate the cosmic GRB rate supposing that the IMF evolves with redshift, and find that we can fit the observation well when the effect of IMF has been taken into account.
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