Explicit modular invariant two-loop superstring amplitude relevant for R-4

In this note we derive an explicit modular invariant formula for the two lo op 4-point amplitude in superstring theory in terms of a multiple integral (7 complex integration variables) over the complex plane which is shown to be convergent. We consider in particular the case of the leading term for v anishing momenta of the four graviton amplitude, which would correspond to the two-loop correction of the R-4 term in the effective Action. The result ing expression is not positive definite and could be zero, although we cann ot see that it vanishes.