Prepotential of N=2 supersymmetric Yang-Mills theories in the weak coupling region

We show how to obtain the explicit form of the low energy quantum effective action for N = 2 supersymmetric Yang-Mills theory in the weak coupling region from the underlying hyperelliptic Riemann surface. This is achieved by evaluating the integral representation of the fields explicitly. We calculate the leading instanton corrections for the group SU(N-c), SO(N) and SP(2N) and find that the one-instanton contribution of the prepotentials for these groups coincide with the one obtained recently by using the direct instanton calculation.