  We calculate the moduli dependent part of string one-loop threshold
corrections to gauge couplings for the heterotic string theory compactified on
abelian toroidal orbifolds, allowing for arbitrary discrete Wilson lines. We
show that the knowledge of threshold corrections for any such compactification
is equivalent to solving a class of integrals. We solve a sub-class of these
integrals and show how any model can be mapped onto this class by fractional
linear transformations of its fixed plane moduli. Modular symmetries of the
final expression are discussed.
