  Let K be a global field. Using natural spaces of functions on the adele ring
and the idele class group of K, we construct a virtual representation of the
idele class group of K whose character is equal to the Weil distribution that
occurs in Andre Weil's Explicit Formula. Hence this representation encodes
information about the distribution of the prime ideals of K, and it is a
spectral interpretation for the poles and zeros of the L-function. It is
closely related to the spectral interpretation of Alain Connes.
