Algebraic Function Fields over Finite Constant Fields

In the previous chapters we developed the theory of algebraic function fields over an arbitrary perfect constant field K. We would now like to consider in greater detail the case of a finite constant field. Observe that a finite field is perfect, so that all results from Chapters 3 and 4 apply. We will mainly be interested in the places of degree one of a function field over a finite field. Their number is finite and can be estimated by the Hasse-Weil Bound (see Theorem 5.2.3). This bound has many number-theoretical implications, and it plays a crucial role in the applications of algebraic function fields to coding theory, cf. Chapter 8 and 9.