| Unit name | Analytic Number Theory |
|---|---|
| Unit code | MATHM0007 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Tim Browning |
| Open unit status | Not open |
| Pre-requisites |
Complex Function Theory (MATH33000) |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
The study of prime numbers is one of the most ancient and most beautiful topics in mathematics. After reviewing some basic topics in elementary number theory and the theory of Dirichlet characters and Dirchlet L-functions, the main aim of this lecture course will be to show how the power of complex analysis can be used to shed light on irregularities in the sequence of primes. The course will build up to a proof of the Prime Number Theorem, with significant attention paid to developing the theory of the Riemann zeta function. The course will build up to a description of the Riemann Hypothesis, which is arguably the most important unsolved problem in modern mathematics.
