Topics to be covered:

• Dirichlet's Theorem on primes in progressions, Dirichlet L-functions
• Binary quadratic forms and Dirichlet's class number formula
• arithmetic of quadratic extensions of the rationals
• Class numbers of imaginary quadratic fields

Schedule:

Prerequisites:

I will assume knowledge of the basic course in number theory and the course "theory of functions of a complex variable 1" (0366-2123-04)

Suggested reading:

• T. Apostol, Introduction to Analytic Number Theory.
• H. Cohn, Advanced Number Theory
• H. Davenport, Multiplicative Number Theory.
• E. Landau, Elementary Number Theory .

Handouts:

• Pell's equation
• The mass formula

Homework:

• Assignment 1, due May 28 2008
• Assignment 2, due June 11 2008
• Assignment 3, due June 18 2008
• Assignment 4, due June 25 2008
• Assignment 5, due July 2, 2008

Take-home exam, due July 30, 2008