After more than 40 years from their discovery, the long-lasting tension between predictions and observations of GRBs prompt emission spectra starts to be solved. We found that the observed spectra can be produced by the synchrotron process, if the emitting particles do not completely cool. Evidence for incomplete cooling was recently found in Swift GRBs spectra with prompt observations down to 0.5 keV (Oganesyan et al. 2017, 2018), characterized by an additional low-energy break. In order to search for this break at higher energies, we analysed the 10 long and 10 short brightest GRBs detected by the Fermi satellite in over 10 years of activity. We found that in 8/10 long GRBs there is compelling evidence of a low energy break (below the peak energy) and the photon indices below and above that break are remarkably consistent with the values predicted by the synchrotron spectrum (-2/3 and -3/2, respectively). None of the ten short GRBs analysed shows a break, but the low energy spectral slope is consistent with -2/3. Within the framework of the GRB standard model, these results imply a very low magnetic field in the emission region, at odds with expectations. I also present the spectral evolution of GRB 190114C, the first GRB detected with high significance by the MAGIC Telescopes, which shows the compresence (in the keV-MeV energy range) of the prompt and of the afterglow emission, the latter rising and dominating the high energy part of the spectral energy range.
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