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

Schedule:

Prerequisites:

I will assume knowledge of the first semester courses in real and complex variables, and the basic course in number theory.

Suggested reading:

• H. Davenport, Multiplicative Number Theory.
• T. Apostol, Introduction to Analytic Number Theory.