FERMI constraints on the high energy, ~1 GeV, emission of long gamma ray bursts

Aims. We investigate the constraints imposed on the luminosity function (LF) of long duration gamma ray bursts (LGRBs) by the flux distribution of bursts detected by the GBM at ~1 MeV, and the implications of the non detection of the vast majority, ~95%, of the LGRBs at higher energy, ~1 GeV, by the LAT detector.