Literature:
Examination:
There will be three compulsory assignments during the course,
and a final written exam at the end of the course.
Your total grade on the course will mainly be decided from your total score on
the home assignments, but you also need to pass the final written exam.
Each home assignment can give 50 points, and the total score on the final exam is 40 points;
thus the total score is 150+40=190 points.
As a guideline for the final grade, a total score above 150 will
typically result in the grade 5; a total score between 115 and 149 in the grade 4,
a total score between 80 and 114 in the grade 3, and a total score below 80
will result in fail.
But note that you also need to pass the final exam (i.e., get above 18 points on it)
in order to pass the course.
Regarding the home assignments:
You are free to cooperate with other students and to read whatever literature you can find about the subject.
You are also welcome to ask me (the teacher) for further hints and suggestions on how to attack the problems.
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!
Preliminary plan of lectures:
ZOOM alternative: The lectures should - hopefully - also be possible to follow, to some extent, on https://uu-se.zoom.us/j/65898322750.
Date | Time | Place | Topic | References |
---|---|---|---|---|
1. Wed, 1/9 | 8-10 | 12167 | Introduction | |
2. Thu, 2/9 | 8-10 | 12167 | Primes in arithmetic progressions | LN Sec 1, Baker 15.3-5 |
3. Mon, 6/9 | 8-10 | 4003 | Infinite products | LN Sec 2, SS Ch 5.3 |
4. Thu, 9/9 | 8-10 | 4004 | Summation by parts; Dirichlet series | LN Sec 3, Baker 13.4 |
5. Mon, 13/9 | 8-10 | 11167 | Theory: Finish lecture 4.
Examples/problem solving: Problems 2.1, 2.2, 2.7. 2.8 in LN (9 Sept: I added problems 2.7 and 2.8 in LN; please click 'reload' to get the updated version of LN) |
|
6. Wed, 15/9 | 8-10 | 12167 | Examples/problem solving: Problems 2.1, 2.2, 3.4, 3.5 in LN
- Since I didn't get time to discuss all these problems, here are solution suggestions for 2.2, 3.4, 3.5. Theory: Dirichlet characters; Fourier analysis on finite abelian groups |
LN Sec 4, Baker 15.3 |
7. Mon, 20/9 | 8-10 | 12167 |
Theory: Finish on Dirichlet characters.
Some more examples |
|
8. Thu, 23/9 | 8-10 | 12167 | The distribution of the primes | LN Sec 6, Baker 13.1-6 |
9. Mon, 27/9 | 8-10 | 12167 | The prime number theorem | LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 |
10. Thu, 30/9 | 8-10 | 12167 | The prime number theorem | LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 |
11. Mon, 4/10 | 8-10 | 12167 | The prime number theorem | LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 |
12. Thu, 7/10 | 8-10 | 4004 | The Gamma function | LN Sec 8; SS Ch 6.1 |
13. Mon, 11/10 | 10-12 | 4004 | The functional equation | LN Sec 9; SS Ch 6.2, Baker 14.2 |
14. Thu, 14/10 | 8-10 | 12167 | Examples/problem solving: Problems 8.1,8.2,8.3,8.4, 9.1(a) and 9.4(d) in LN (perhaps also 9.4(a)-(c))
(13 Oct: I corrected slightly in Problems 9.4(b),(c); please click 'reload' to get the updated version of LN) |
|
15. Mon, 18/10 | 10-12 | 12167 | The explicit formula for psi(x) | LN Sec 13 |
16. Thu, 21/10 | 8-10 | 12167 | Zero-free region; PNT with error term | LN Sec 11, Baker 14.6, 15.2 |
17. Wed, 27/10 | 8-10 | 12167 | Binary quadratic forms | LN Sec 5, Baker Ch 5 |
18. Mon, 1/11 | 8-10 | 12167 | Dirichlet's class number formula | LN Sec 5 (Baker 15.6) |
19. Wed, 10/11 | 8-10 | 12167 | Dirichlet's class number formula (cont'd) | |
20. Wed, 17/11 | 8-10 | 12167 | The Jacobi Theta function | SS Ch 10 (my lecture notes) |
21. Mon, 22/11 | 8-10 | 12167 | Examples/problem solving: The problem on p.5 here, and
problem 5.4 in LN.
Probably I will also have time to start on the next lecture (sums of squares). |
|
22. Fri, 26/11 | 8-10 | 12167 | Sums of squares | SS Ch 10 (Baker 5.4-5) |
23. Mon, 6/12 | 8-10 | 12167 | The large sieve | LN Sec 20,21 (Baker Ch 16) |
24. Wed, 8/12 | 8-10 | 12167 | The large sieve | LN Sec 20,21 (Baker Ch 16) |
25. Wed, 15/12 | 8-10 | 12167 | The large sieve; the Bombieri-Vinogradov theorem | LN Sec 20,21 (Baker Ch 16) |