  In this note we show that by fixing the multiloop Green function in the
closed bosonic string to be Arakelov's Green function, one obtains
factorization of scattering amplitudes with a softly emitted dilaton to the
same level as with a graviton to all loop order. This extends our previous
analysis at one loop to all loop orders and confirms that some high-energy
quantum symmetry in the bosonic string protects the factorization of amplitudes
with softly emitted dilatons.
