  Using our previous construction of Eisenstein-like automorphic forms we
derive formulae for the perturbative and non-perturbative parts for any group
and representation. The result is written in terms of the weights of the
representation and the derivation is largely group theoretical. Specialising to
the E_{n+1} groups relevant to type II string theory and the representation
associated with node n+1 of the E_{n+1} Dynkin diagram we explicitly find the
perturbative part in terms of String Theory variables, such as the string
coupling g_d and volume V_n. For dimensions seven and higher we find that the
perturbation theory involves only two terms. In six dimensions we construct the
SO(5,5) automorphic form using the vector representation. Although these
automorphic forms are generally compatible with String Theory, the one relevant
to R^4 involves terms with g_d^{-6} and so is problematic. We then study a
constrained SO(5,5) automorphic form, obtained by summing over null vectors,
and compute its perturbative part. We find that it is consistent with String
Theory and makes precise predictions for the perturbative results. We also
study the unconstrained automorphic forms for E_6 in the 27 representation and
E_7 in the 133 representation, giving their perturbative part and commenting on
their role in String Theory.
