An introduction to classical results in analytic number theory, presenting fundamental theorems with detailed proofs and highlighting the tight connections between them. Topics covered might include: the prime number theorem, Dirichlet L-functions, zero-free regions, sieve methods, representation by quadratic forms, and Gauss sums. Prerequisites: MAT335 (Complex Analysis) and MAT345 (Algebra I).

# Course MAT415

## Analytic Number Theory

There will be weekly problem sets and reading assignments. The problem sets count for 75% of the course grade. The final exam counts as the remaining 25%.

Texts:

- Multiplicative Number Theory, by H. Davenport
- Multiplicative Number Theory: I. Classical Theory, by H. Montgomery and R. Vaughan