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 maximal score on the final exam is 40 points;
thus the maximal 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 at least 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!
Written exam: Fri 5/1-2024, 8.00-13.00.
List of possible exam questions: here. Some old exams: Exam Jan 2022; Exam June 2022.
Preliminary plan of lectures:
Date | Time | Place | Topic | References |
---|---|---|---|---|
1. Mon, 28/8 | 8-10 | 80115 | Introduction | |
2. Wed, 30/8 | 8-10 | 11167 | Primes in arithmetic progressions | LN Sec 1, Baker 15.3-5 |
3. Mon, 4/9 | 8-10 | 4003 | Infinite products | LN Sec 2, SS Ch 5.3 |
4. Thu, 7/9 | 8-10 | 2003 | Summation by parts; Dirichlet series | LN Sec 3, Baker 13.4 |
5. Mon, 11/9 | 8-10 | 2003 | Examples/problem solving: Problems 2.1, 2.2, 2.7. 2.8, 3.4, 3.5, 3.13 in LN | solution sketches |
6. Wed, 13/9 | 8-10 | 4003 | Dirichlet characters (Fourier analysis on finite abelian groups) | LN Sec 4.1-6, Baker 15.3 |
7. Mon, 18/9 | 8-10 | 11167 | The distribution of the primes | LN Sec 6, Baker 13.1-6 |
8. Wed, 20/9 | 8-10 | 12167 | The prime number theorem | LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 |
9. Thu, 28/9 | 8-10 | 11167 | The prime number theorem | LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 |
10. Thu, 5/10 | 10-12 | 11167 | The prime number theorem [Half of the lecture: Prof. Dennis Hejhal will present a curiously simple proof of the PNT.] | LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 |
11. Thu, 12/10 | 8-10 | 2003 | Examples/problem solving: Problems 3.13, 4.1, 4.3, 6.1, 6.2, 6.4, 6.6, 7.1, 7.2, 7.4, 7.7 in LN.
- I will probably start by discussing problem 7.4, with particular focus on part (c), which I will discuss together with LN Theorem 7.10. |
solution sketches |
12. Thu, 19/10 | 10-12 | 12167 | The Gamma function | LN Sec 8; SS Ch 6.1 |
13. Thu, 26/10 | 8-10 | 12167 | The functional equation | LN Sec 9; SS Ch 6.2, Baker 14.2 |
14. Tue, 31/10 | 8-10 | 12167 | The explicit formula for psi(x) | LN Sec 13 |
15. Mon, 6/11 | 10-12 | 4005 | Zero-free region; PNT with error term | LN Sec 11, Baker 14.6, 15.2 |
16. Mon, 13/11 | 8-10 | 12167 | Examples/problem solving: Problems 8.1, 8.3, 8.4, 8.5, 8.6, 9.1, 9.2(a), 9.5, 13.4, 15.1, 16.3 in LN. | solution sketches |
17. Wed 15/11 | 8-10 | 11167 | Binary quadratic forms | LN Sec 5, Baker Ch 5 |
18. Mon 20/11 | 8-10 | 12167 | Dirichlet's class number formula | LN Sec 5 (Baker 15.6) |
19. Mon 27/11 | 8-10 | 11167 | The Jacobi Theta function | SS Ch 10 |
20. Wed 29/11 | 8-10 | 12167 | Sums of squares | SS Ch 10 (Baker 5.4-5) |
21. Tue 5/12 | 8-10 | 12167 | Examples/problem solving: Problems 5.4, 5.5, 5.6, 8.9, 9.1(b),(c) in LN. | solution sketches |
22. Mon 11/12 | 8-10 | 12167 | The large sieve | LN Sec 20,21 (Baker Ch 16) |
23. Thu 14/12 | 8-10 | 12167 | The large sieve | LN Sec 20,21 (Baker Ch 16) |
24. Tue 19/12 | 8-10 | 12167 | The large sieve (and the Bombieri-Vinogradov theorem) | LN Sec 20,21 (Baker Ch 16) |
25. Thu 21/12 | 10-12 | 11167 | The large sieve; the Bombieri-Vinogradov theorem | LN Sec 20,21 (Baker Ch 16) |