MMA340 Analytic Number Theory Spring 25
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 20/1 | Short introduction. Arithmetic functions. | |
| Tuesday 21/1 | Arithmetic functions | |
| Thursday 23/1 | Arithmetic functions | |
| Monday 27/1 | Arithmetic functions | |
| Tuesday 28/1 | Elementary results on prime counting | |
| Thursday 30/1 | 7 | Elementary results on prime counting |
| Monday 3/2 | 7 | Elementary results on prime counting |
| Tuesday 4/2 | 1,8 | Dirichlet series |
| Wednesday 5/2 | 1,8 | Dirichlet series |
| Thursday 6/2 | Dirichlet series and Euler products | |
| Monday 17/2 | Dirichlet series and Euler products | |
| Tuesday 18/2 | The Riemann zeta function | |
| Thursday 20/2 | 17-18 | The prime number theorem |
| Monday 24/2 | 10-11,17-18 | The prime number theorem |
| Tuesday 25/2 | 8-10 | The Riemann zeta function |
| Wednesday 26/2 | 11-13 | The Riemann zeta function |
| Thursday 27/2 | 15,17,18 | The prime number theorem |
| Monday 3/3 | Dirichlet characters and Dirichlet L-functions | |
| Tuesday 4/3 | Dirichlet characters and Dirichlet L-functions | |
| Thursday 6/3 | 1,4 | The prime number theorem in arithmetic progressions |
| Monday 10/3 | 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 from 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. It is also not allowed to use AI tools to solve the problems or to formulate the solutions!
Course summary:
| Date | Details | Due |
|---|---|---|