  Supersymmetric theories of gravity can exhibit surprising hidden symmetries
when considered on manifolds that include a torus. When the torus is of large
dimension these symmetries can become infinite-dimensional and of Kac-Moody
type. When taking quantum effects into account the symmetries become discrete
and invariant functions under these symmetries should play an important role in
quantum gravity. The new results here concern surprising simplifications in the
constant terms of very particular Eisenstein series on the these Kac-Moody
groups. These are exactly the cases that are expected to arise in string
theory.
