Math 9062 : Analytic Number Theory

Summer 2018.

Course description : The goal of this course is to prove Dirichlet's theorem on primes in an arithmetic progression. We will begin by recalling/introducing analytic functions of one complex variable and discussing their main properties. The hero of the story is the Dirichlet L-function, an example of an analytic function. The main theorem of the course is deduced from a non-vanishing theorem on Dirichlet L-functions. We will mostly follow Serre's book, A course in Arithmetic. If we have time we will discuss modular forms in the last part of the course. What we won't cover (but probably should) is the prime number theorem.


Meeting Times and location :  MWF 10:30-11:50, MC 107.

Marks : 2 assignments worth 25% each.

            Final exam worth 50%