Introduction to Analytic Number Theory
Topics to be covered:
- Dirichlet's Theorem on primes in progressions, Dirichlet L-functions
- Binary quadratic forms and Dirichlet's class number formula
- Riemann's zeta-function
- The Prime Number Theorem
- The Riemann Hypothesis and its consequences
- Sieve methods
- Class numbers of imaginary quadratic fields and Siegel's theorem
- GRH and its applications
Tuesday, 15-18, Shenkar 114
I will assume knowledge of the first semester courses in real and
complex variables, and the basic course in number theory.
- H. Davenport, Multiplicative Number Theory.
- T. Apostol, Introduction to Analytic Number Theory.
Zeev Rudnick's Homepage.