The 1.4 GHz light curve of GRB 970508

We report on Westerbork 1.4 GHz radio observations of the radio counterpart to gamma -ray burst GRB 970508, between 0.80 and 138 days after this event. The 1.4 GHz light curve shows a transition from optically thick to thin emission between 39 and 54 days after the event. We derive the slope p of the spectrum of injected electrons ( dN/d gamma e~ gamma ^{-p}e ) in two independent ways, which yield values very close to p=2.2 . This is in agreement with a relativistic dynamically near-adiabatic blast-wave model whose emission is dominated by synchrotron radiation and in which a significant fraction of the electrons cool fast.