Analytic Number Theory Spring 2019

Boston College, Spring 2019

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 to some 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
Sieve methods and their application

Prerequisites

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

I will assume a working knowledge of basic courses in real and 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
R. C. Vaughan, The Hardy-Littlewood method <\li>

Schedule

MWF 9-10

Room: Maloney 560

Homework

There will be periodic homework assignments posted here.

Assignments

Problem set 1 in PDF (due Fri Feb 15)
Problem set 2 in PDF (due Mon Feb 25)
Problem set 3 in PDF (due Mon Mar 25)

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