Analytic Number Theory

Boston College, Spring 2013

The aim of this course is to learn some of the useful techniques of analytic number theory. We will do this by considering their application classical problems such as the distribution of prime numbers and counting the number of integer solution to Diophantine equations. In particular some of the topics we will cover are

• Arithmetic functions
• Elementary approach to distribution of prime numbers
• Riemann Zeta function, Dirichlet L-functions and their application to distribution of prime numbers ,
• The circle method and its applications
• Some Sieve methods

Prerequisites

The course is intended for graduate students; interested undergraduate students are also welcome.

I will assume knowledge of basic courses in complex analysis, linear algebra, and group theory.

Bibliography

• T. Apostol, Introduction to Analytic Number Theory
• M. Ram Murty, Problems in Analytic Number Theory
• H. Iwaniec and E. Kowalski, Analytic Number Theory

Schedule

MWF 1-2

Room: Stokes 101N

Homework

There will be periodic homework assignments posted here.

Assignments

1. Assignment 1, due date: Feb. 8, 2013.
2. Assignment 2, due date: Feb. 22, 2013.
3. Assignment 3, due date: March. 15, 2013.
4. Assignment 4, due date: Apr. 5, 2013.
5. Assignment 5, due date: May. 1, 2013.