  By giving the definition of the sum of a series indexed by a set on which a
group acts, we prove that the sum of the series that defines the Riemann zeta
function, the Epstein zeta function, and a few other series indexed by $\Z^k$
has an intrinsic meaning as a complex number, independent of the requirements
of analytic continuation.
  The definition of the sum requires nothing more than algebra and the concept
of absolute convergence. The analytical significance of the algebraically
defined sum is then explained by an argument that relies on the Poisson formula
for tempered distributions.
