%0 Journal Article %T The 1.4 GHz light curve of GRB 970508 %A T. J. Galama %A R. A. M. J. Wijers %A M. Bremer %A P. J. Groot %A R. G. Strom %A A. G. de Bruyn %A C. Kouveliotou %A C. R. Robinson %A J. van Paradijs %J Physics %D 1998 %I arXiv %R 10.1086/311424 %X 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 ($dN/d\gamma_{e}\propto\gamma_{e}^{-p}$) 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. %U http://arxiv.org/abs/astro-ph/9804190v1