MMA340 Analytic Number Theory Spring 21
This page contains the program of the course. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
The course will be given via digital meetings in Zoom. The lectures will be given at the times specified in the course schedule in TimeEdit. Conducting the digital meetings in a good way will be demanding for all of us. This course is full of long and rather technical arguments and we will have to do our best to stay focused in the online format.
It will be helpful if your microphones are muted when you are not talking or asking questions. It might also be helpful to connect from a physical location that is quiet and peaceful, and to close programs and tabs in your browser that are not needed in connection to the lectures.
Program
The schedule of the course is in TimeEdit.
Note that minor changes might occur in the program.
Lectures
Link to the course Zoom room: https://chalmers.zoom.us/j/61013930947
(The password will be distributed in a course announcement.)
| Day | Sections | Content |
|---|---|---|
| Monday 22/3 | Short introduction. Arithmetic functions. | |
| Tuesday 23/3 | Arithmetic functions | |
| Thursday 25/3 | Arithmetic functions | |
| Monday 12/4 | Arithmetic functions | |
| Tuesday 13/4 | Elementary results on prime counting | |
| Thursday 15/4 | Elementary results on prime counting | |
| Monday 19/4 | 7 | Elementary results on prime counting |
| Tuesday 20/4 | 1,8 | Dirichlet series |
| Thursday 22/4 | 1,8 | Dirichlet series |
| Monday 26/4 | Dirichlet series and Euler products | |
| Tuesday 27/4 | Dirichlet series and Euler products | |
| Thursday 29/4 | The Riemann zeta function | |
| Monday 3/5 | 17-18 | The prime number theorem |
| Tuesday 4/5 | 10-11,17-18 | The prime number theorem |
| Thursday 6/5 | 8-10 | The Riemann zeta function |
| Monday 10/5 | 11-13 | The Riemann zeta function |
| Tuesday 11/5 | 15,17,18 | The prime number theorem |
| Monday 17/5 | Dirichlet characters and Dirichlet L-functions | |
| Tuesday 18/5 | Dirichlet characters and Dirichlet L-functions | |
| Thursday 20/5 | 1,4 | The prime number theorem in arithmetic progressions |
| Monday 24/5 | 14,20 | The prime number theorem in arithmetic progressions |
Recommended exercises
| Week | Exercises |
|---|---|
| 1 | Exercise sheet 1 |
| 2 | Exercise sheet 2 |
| 3 | Exercise sheet 3 |
| 4 | Exercise sheet 4 |
| 5 | Exercise sheet 5 |
| 6 | Exercise sheet 6 |
| 7 | Exercise sheet 7 |
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 |
|---|---|---|