Threshhold Corrections in $K3\times T2$ Heterotic String Compactifications

We consider compactifications of the heterotic string on $K3 \times T2$ so that the resulting theory in $d = 4$ space-time dimensions has $N = 2$ supersymmetry. The gravitational and gauge coupling constants of the low-energy effective theory receive threshold corrections from loops of super-heavy string states. We calculate these corrections for the case when the $K3$-surface is a ${\bf Z}_n$ orbifold of a four torus $T4$. The results are used to determine the one-loop prepotential ${\cal F}_0^{(1)}$ for the vector multiplets and the gravitational coupling ${\cal F}_1^{(1)}$.