COUNTING CURVES WITH MODULAR-FORMS

We consider the type IIA string compactified on the Calabi-Yau space g iven by a degree 12 hypersurface in the weighted projective space P-4( 1,1,2,2,6). We express the prepotential of the low-energy effective su pergravity theory in terms of a set of functions that transform covari antly under PSL(2,Z) modular transformations. These functions are then determined by monodromy properties, by singularities at the massless monopole point of the moduli space, and by S <-> T exchange symmetry.