In spring 2023 I am teaching Math 191 (Analytic Number Theory).
Office hours: W 11:00A-12:20P and 1:30P-2:50P
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. You should read the textbook on your own.
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