The effect of the experimental liquid-glass transition on the dielectric relaxation of three amorphous polymers is investigated by means of frequency and time domain dielectric spectroscopies. By means of the time domain experiments, the dynamics of both the supercooled melt and the glassy polymer are characterized. The structural "state" of the glassy polymer is determined by means of differential scanning calorimetry. It is found that the relaxation behavior can be well described by the Kohlrousch-Williams-Watts (KWW) relaxation function above and below T-g. The temperature dependence of the characteristic time scale shows a clear crossover from a Volgel-Fulcher behavior toward an Arrhenius behavior in the liquid-glass transition range. The whole behavior, which extends over 10 decades in time scale, can be fully described by the Adam and Gibbs theory framework, if a slow change of the configurational entropy in the glassy state is allowed. On the other hand, when the system falls out of equilibrium, the KWW shape parameter, beta, appears to be slightly higher than the one corresponding to the supercooled liquid. The behavior of beta around the glass transition leads us to interpret the relaxation shape as a consequence of a narrow distribution of strongly correlated relaxation processes.