ABSTRACT
CHAPTER 8
This chapter provides a self-contained introduction to abstract analytic number theory. It is basic for the analytic theory of non-unique factorizations in monoids of algebraic numbers and algebraic functions, which are presented in Chapter 9. The basic structures of our investigations are formations [D,H, | · |], consisting of a reduced Krull monoid H with finite class group, a monoid D of divisors for H, and a norm function | · | : D → N having an arithmetically reasonable behavior. The conditions imposed on the norm function are based on the axioms used in the books of J. Knopfmacher and W.-B. Zhang [281], [282], [283].
