  Tests of duality between heterotic strings on $K3\times T^2$ (restricted on
certain Narain moduli subspaces) and type IIA strings on K3-fibered Calabi-Yau
threefolds are attempted in the weak coupling regime on the heterotic side by
identifying pertinent modular forms related to the computations of string
threshold corrections. Concretely we discuss in parallel the three cases
associated with Calabi-Yau manifolds $(A):X(6,2,2,1,1)_{2}^{-252}$,
$(B):X(12,8,2,1,1)_{3}^{-480}$ and $(C):X(10,3,3,2,2)_{4}^{-132}$ on the type
IIA side.
