These lecture notes are the only required reading for the course. Homework questions are included in the notes - please see the assignments page to find out when they were assigned.

- Introduction to the course (PDF)
- The prime number theorem (PDF)
- Dirichlet series and arithmetic functions (PDF)
- Dirichlet characters and L-functions (PDF)
- Primes in arithmetic progressions (PDF)
- The functional equation for the Riemann zeta function (PDF)
- Functional equations for Dirichlet L-functions (PDF)
- Error bounds in the prime number theorem (PDF)
- More on the zeroes of zeta (PDF)
- von Mangoldt's formula (PDF)
- Error bounds in the prime number theorem in arithmetic progressions (PDF)
- Revisiting the sieve of Eratosthenes (PDF)
- Brun's combinatorial sieve (PDF)
- The Selberg sieve (PDF)
- Applying the Selberg sieve (PDF)
- Introduction to large sieve inequalities (PDF)
- A multiplicative large sieve inequality (PDF)
- The Bombieri-Vinogradov theorem (statement) (PDF)
- The Bombieri-Vinogradov theorem (proof) (PDF)
- Prime k-tuples (PDF)
- Small gaps between primes (after Goldston-Pintz-Yildirim) (PDF)

(see also the article by Soundararajan and the article by Goldston, Motohashi, Pintz, and Yildirim) - Small gaps between primes (proofs) (PDF)

(again, see article by Goldston, et al.) - Artin L-functions and the Chebotarev density theorem (PDF)
- Elliptic curves and their L-functions (PDF)
- The Sato-Tate distribution (PDF)