Using the technique of
compact rational subgroup approximations to unitary representations on a
nilmanifold, we justify the evaluation of a distribution at certain rational points of a
group. This method allows us to give meaning to a distributional identity between
theta-like functions at discrete points in the group. The identity itself arises from the
equivalence of certain representations of the group. In attempting to compute an
intertwining constant that is present, we are also able to show the existence of
distributions that behave like the classical gaussians, i.e., they are eigenfunctions of
the Fourier transform.
