Résumé : It is shown that the observed quantum Hall effect in epitaxial layers of heavily doped n-type GaAs with thickness (50-140 nm) larger the mean free path of the conduction electrons (15-30 nm) and, therefore, with a three-dimensional single-particle spectrum is induced by the electron-electron interaction. The Hall resistance Rxy of the thinnest sample reveals a wide plateau at small activation energy Ea=0.4 K found in the temperature dependence of the transverse resistance Rxx. The different minima in the transverse conductance Gxx of the different samples show a universal temperature dependence (logarithmic in a large range of rescaled temperatures T/T0) that is reminiscent of electron-electron-interaction effects in coherent diffusive transport. © 1999 The American Physical Society.