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
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.
- T. Apostol, Introduction to Analytic Number Theory
- M. Ram Murty, Problems in Analytic Number Theory
- H. Iwaniec and E. Kowalski, Analytic Number Theory
Room: Stokes 101N
There will be periodic homework assignments posted here.
Assignment 1, due date: Feb. 8, 2013.
Assignment 2, due date: Feb. 22, 2013.
Assignment 3, due date: March. 15, 2013.
Assignment 4, due date: Apr. 5, 2013.
Assignment 5, due date: May. 1, 2013.
Contact me at: firstname.lastname@example.org, Office : Carney 268, tel: (617) 552-6588
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