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://uuse.zoom.us/j/65898322750.
Date  Time  Place  Topic  References 

1. Wed, 1/9  810  12167  Introduction  
2. Thu, 2/9  810  12167  Primes in arithmetic progressions  LN Sec 1, Baker 15.35 
3. Mon, 6/9  810  4003  Infinite products  LN Sec 2, SS Ch 5.3 
4. Thu, 9/9  810  4004  Summation by parts; Dirichlet series  LN Sec 3, Baker 13.4 
5. Mon, 13/9  810  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  810  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  810  12167 
Theory: Finish on Dirichlet characters.
Some more examples 

8. Thu, 23/9  810  12167  The distribution of the primes  LN Sec 6, Baker 13.16 
9. Mon, 27/9  810  12167  The prime number theorem  LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 
10. Thu, 30/9  810  12167  The prime number theorem  LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 
11. Mon, 4/10  810  12167  The prime number theorem  LN Sec 7; Baker Ch 14 and 15.1; SS Ch 7 
12. Thu, 7/10  810  4004  The Gamma function  LN Sec 8; SS Ch 6.1 
13. Mon, 11/10  1012  4004  The functional equation  LN Sec 9; SS Ch 6.2, Baker 14.2 
14. Thu, 14/10  810  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  1012  12167  The explicit formula for psi(x)  LN Sec 13 
16. Thu, 21/10  810  12167  Zerofree region; PNT with error term  LN Sec 11, Baker 14.6, 15.2 
17. Wed, 27/10  810  12167  Binary quadratic forms  LN Sec 5, Baker Ch 5 
18. Mon, 1/11  810  12167  Dirichlet's class number formula  LN Sec 5 (Baker 15.6) 
19. Wed, 10/11  810  12167  Dirichlet's class number formula (cont'd)  
20. Wed, 17/11  810  12167  The Jacobi Theta function  SS Ch 10 (my lecture notes) 
21. Mon, 22/11  810  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  810  12167  Sums of squares  SS Ch 10 (Baker 5.45) 
23. Mon, 6/12  810  12167  The large sieve  LN Sec 20,21 (Baker Ch 16) 
24. Wed, 8/12  810  12167  The large sieve  LN Sec 20,21 (Baker Ch 16) 
25. Wed, 15/12  810  12167  The large sieve; the BombieriVinogradov theorem  LN Sec 20,21 (Baker Ch 16) 