L-Functions of Number Fields

In this chapter, we shall obtain universality for many classical L-functions, including Dedekind zeta-functions as well as Hecke and Artin L-functions. Further, we shall briefly discuss the arithmetic axioms in the definition of S with respect to the Langlands program. We give only a sketch of the analytic theory of all these L-functions and refer to Bump et al. [47] for further details. For details from algebraic number theory we refer to Heilbronn's survey [129], the monographs of Murty and Murty [270], of Neukirch [279], and, last but not least, Stark's article [337].