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. Methods. We find a LF that is consistent with those determined by BATSE and Swift. The non detections by LAT set upper limits on the ratio R of the prompt fluence at ~1 GeV to that at ~1 MeV. The upper limits are more stringent for brighter bursts, with upper limits on R