Understanding the Rie- mann hypothesis and basic theory of univalent functions

Abstract

In this thesis, we study the following topics in complex analysis:-
(1) Riemann Mapping theorem.
(2) Riemann’s zeta function.
(3) Basic univalent function theory.
We also study the famous unsolved problem, the Riemann Hypothesis during the course and establish a relation between Riemann zeta function and number theory through Eu-
ler’s theorem. Lastly, we focus on some basic univalent function theory, which leads us to understand the Bieberbach conjecture.