  We propose $SL(2,Z)$ (and $SL(3,Z)$) invariant conjectures for all $R^4
H^{4g-4}$ couplings of Type IIB strings on $R^{10}$ (and $R^{8}\times T^2$),
generalizing conjectures of Green and Gutperle (and Kiritsis and Pioline) for
the $R^4$ coupling. A strong check for our conjectures is that on $T^2$ at weak
coupling, they reproduce the multiloop scattering amplitudes which had been
previously computed using N=2 strings in the N=4 topological formalism.
Applications to $(p,q)$ string production in a background $H$ field,
generalizing Schwinger's computation for pair production in constant $F$ field,
are suggested.
