Mu-theta functions

Abstract

Using the technique of compact rational subgroup approximations to unitary representation 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. © 1982, University of California, Berkeley. All Rights Reserved.