MMA340 Analytic Number Theory Spring 23
This page contains the program of the course. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Program
The schedule of the course is in TimeEdit.
Note that minor changes might occur in the program.
In the table below the section numbers refer to sections in Davenport's book Multiplicative number theory.
Lectures
| Day | Sections | Content |
|---|---|---|
| Monday 16/1 | Short introduction. Arithmetic functions. | |
| Tuesday 17/1 | Arithmetic functions | |
| Thursday 19/1 | Arithmetic functions | |
| Monday 23/1 | Arithmetic functions | |
| Tuesday 24/1 | Elementary results on prime counting | |
| Thursday 26/1 | 7 | Elementary results on prime counting |
| Monday 30/1 | 7 | Elementary results on prime counting |
| Tuesday 31/1 | 1,8 | Dirichlet series |
| Thursday 2/2 | 1,8 | Dirichlet series |
| Tuesday 7/2 | Dirichlet series and Euler products | |
| Thursday 9/2 | Dirichlet series and Euler products | |
| Friday 10/2 | The Riemann zeta function | |
| Tuesday 14/2 | 17-18 | The prime number theorem |
| Thursday 16/2 | 10-11,17-18 | The prime number theorem |
| Friday 17/2 | 8-10 | The Riemann zeta function |
| Tuesday 21/2 | 11-13 | The Riemann zeta function |
| Wednesday 22/2 | 15,17,18 | The prime number theorem |
| Friday 24/2 | Dirichlet characters and Dirichlet L-functions | |
| Monday 27/2 | Dirichlet characters and Dirichlet L-functions | |
| Tuesday 28/2 | 1,4 | The prime number theorem in arithmetic progressions |
| Thursday 2/3 | 14,20 | The prime number theorem in arithmetic progressions |
Recommended exercises
Here exercises will appear during the course.
| Week | Exercises |
|---|---|
| 1 | Exercise sheet 1 (final version) |
| 2 | Exercise sheet 2 (final version) |
| 3 | Exercise sheet 3 (final version) |
| 4 | Exercise sheet 4 (final version) |
| 5 | Exercise sheet 5 (final version) |
| 6 | Exercise sheet 6 (final version) |
| 7 | Exercise sheet 7 (final version) |
Assignments
There will be three sets of homework assignments distributed during the course. Each set will consist of 3-5 problems.
PLEASE NOTE: This is to clarify the rules for everybody interested in working with these assignments. You are free to cooperate with other students and to read whatever literature you can find about the subject. However, you are expected to formulate your solutions independently and it is neither allowed to copy from other students nor to copy solutions form any other source! No credit will be given to such solutions and if this happens in a systematic fashion you will be reported for plagiarism.
Course summary:
| Date | Details | Due |
|---|---|---|