  We derive the moduli dependence of the one--loop gauge couplings for
non--vanishing gauge background fields in a four--dimensional heterotic (0,2)
string compactification. Remarkably, these functions turn out to have a
representation as modular functions on an auxiliary Riemann surface on
appropriate truncations of the full moduli space. In particular, a certain kind
of one--loop functions is given by the free energy of two--dimensional solitons
on this surface.
