In fall 2019 I am teaching Math 749 (Analytic Number Theory).
Room change notice: We will have lectures in VV B135 starting 9/9 (Monday)
Our two Problem Sets will be posted here.
Textbook: Multiplicative Number Theory by H. Davenport (Third Edition)
I will cover most contents in the above textbook but probably will not follow it closely in various places. I encourage you to read the textbook on your own.
Problem Set 2 (Part 1) [Extended due date on Dec 9]
Problem Set 2 (Part 2) [Extended due date on Dec 9]
I plan to cover the following topics:
1. Dirichlet's Theorem on primes in progressions
2. Dirichlet L-functions, class numbers
3. Analytic theory: analytic continuation, functional equations and the Prime Number Theorem
4. Non-vanishing of L(1, \chi_d), Siegel's theorem and its ineffectivity
5. The Bombieri-Vinogradov theorem
6. Elementary Sieve
7. Vinogradov's Theorem and his bilinear sieve method
8. Primality testing
9. The Burgess bound
10. Elementary counting in finite fields
Here is the Syllabus.