In spring 2023 I am teaching Math 191 (Analytic Number Theory).

bCourses website

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