We shall be dealing in these lectures with the algebraic aspects of the
theory of algebraic functions of one variable. Since an algebraic function
w(z) is defined implicitly by an equation of the form f (z, w) = 0,
where f is a polynomial, it is understandable that the study of such functions should be possible by algebraic methods. Such methods also have the advantage that the theory can be developed in the most general setting, viz. over an arbitrary field, and not only over field of complex
numbers (the classical case). |