N=2 SUPER YANG-MILLS AND SUBGROUPS OF SL(2,Z)

We discuss SL(2,Z) subgroups appropriate for the study of N = 2 super Yang-Mills with N-f = 2n flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these sub groups. In particular, uniqueness arguments are sufficient to construc t the SU(3) curve, up to two numerical constants, which can be fixed b y making some assumptions about strong coupling behavior. We also disc uss the situation for higher groups. We also include a derivation of t he closed form beta-function for the SU(2) and SU(3) theories without matter, and the massless theories with N-f = n.