SL(2,Z) duality of Born-Infeld theory from non-linear self-dual electrodynamics in 6 dimensions

We reformulate the Born-Infeld action, coupled to an axion and a dilation in a duality manifest way. This action is the generalization of the Schwarz-Sen action for non-linear electrodynamics. We show that this action may be obtained by dimensional reduction on a torus of a self-dual theory in 6 dimensions. The dilaton-axion being identified with the complex structure of the torus. Applications to M-theory and the self-dual IIB three brane are investigated.