The aim of this survey is to outline some basic concepts and results of "abstract" analytic
number theory, with an emphasis on applications to concrete systems arising
in a variety of mathematical fields. Some remarks on more recent investigations
are also included.

Mathematics Subject Classification (1991): 11-02, 11N, 11T55
Keywords: analytic number theory, research exposition, multiplicative
number theory, arithmetic theory of polynomial rings over finite fields, arithmetical
semigroups, semisimple finite rings, Lie, symmetric Riemannian manifolds, finite
topological spaces, finite graphs, zeta functions, number theory



Quaestiones Mathematicae 24(3) 2001, 291-307