Course MAT415

Analytic Number Theory

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).

Description of classes

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