In this program
- Dirichlet series and the Riemann zeta function
- Prime number theorem (proof outline)
- L-functions
- Dirichlet's theorem on primes in arithmetic progressions
- Modular forms (introduction)
- Elliptic curves: Mordell–Weil theorem (statement)
Analytic methods
Dirichlet series and the Riemann zeta function
Number theory · Theoretical / proof-based
Topic
Dirichlet series and the Riemann zeta function
Graduate Number Theory — scope drawn from open graduate number theory notes and typical US graduate number theory syllabi.