  In this paper we continue to study the Reidemeister zeta function. We prove
P\'olya -- Carlson dichotomy between rationality and a natural boundary for
analytic behavior of the Reidemeister zeta function for a large class of
automorphisms of Abelian groups. We also study dynamical representation theory
zeta functions counting numbers of fixed irreducible representations for
iterations of an endomorphism. The rationality and functional equation for
these zeta functions are proven for several classes of groups. We find a
connection between these zeta functions and the Reidemeister torsions of the
corresponding mapping tori. We also establish the connection between the
Reidemeister zeta function and dynamical representation theory zeta functions
under restriction of endomorphism to a subgroup and to a quotient group.
