Description

The Riemann zeta function lies at the heart of analytic number theory. ''The Riemann Hypothesis'', arguably one of the most famous open problems in number theory, has driven much of the modern day analytic number theory. In the recent years, connections of the Riemann zeta function has been established from the links with distribution of primes, random matrix theory, representation theory to mathematical physics.

This project will focus on providing an introduction to Analytic Number Theory by studying the theory Riemann zeta function. We will consider some of the following aspects of the theory:

• Definition of the Riemann zeta function and its analytic continuation
• Links to the distribution of primes
  
• Approximate functional equation
  
• Understanding the intricacy of ''The Riemann Hypothesis'' and some of its possible implications.
• Some further applications
  

Prerequisites

Resources