  General conjectures about the SL(2,Z) modular transformation properties of
N=4 super-Yang-Mills correlation functions are presented. It is shown how these
modular transformation properties arise from the conjectured duality with IIB
string theory on AdS_5 x S^5. We discuss in detail a prediction of the AdS
duality: that N=4 field theory, in an appropriate limit, must exhibit bonus
symmetries, corresponding to the enhanced symmetries of IIB string theory in
its supergravity limit.
