  The modular invariant coefficient of the D^{2k} {\cal{R}}^4 term in the
effective action of type IIB superstring theory is expected to satisfy Poisson
equation on the fundamental domain of SL(2,Z). Under certain assumptions, we
obtain the equation satisfied by D^{10} {\cal{R}}^4 using the tree level and
one loop results for four graviton scattering in type II string theory. This
leads to the conclusion that the perturbative contributions to D^{10}
{\cal{R}}^4 vanish above three loops, and also predicts the coefficients at two
and three loops.
