Alladi Ramakrishnan Hall

Complex analytic functions of one and many variables

J. Oesterle

University of Paris VI

In this course, we shall start by studying rings of formal
and convergent power series, in one and many variables. We shall
investigate harmonic functions and the Dirichlet problem.
After reviewing the classical theory of holomorphic functions
of one variable, we shall describe the foundations of the theory
of Riemann surfaces, both open and compact, and then give an
introduction to higher dimensional complex analytic manifolds.