MATH4850 - TOPICS IN NUMBER THEORY  

Math4850A/5850A/7850A - Topics in number theory
Fall 2011

Instructor Nathan Ng email: nathan.ng@uleth.ca phone: 403-329-5118
Lectures Tuesday, Thursday 10:50-12:05 room: TBA
Office hours Tuesday
Thursday
or by appointment 		1:15 - 2:15 pm
1:15 - 2:15 pm 		office: C558

Course syllabus (to be posted)

GENERAL COURSE DESCRIPTION:

In this course we will study the finer theory of prime numbers. For instance, is it possible to determine if a given integer is prime or not. A related question is how many prime numbers are there less than a given large number like 10^{1000}?

The theory used to study these questions is called analytic number theory and was invented by the great mathematicians Dirichlet in 1837 and by Riemann in 1859. We shall study in depth the relationship between prime numbers and the Riemann zeta function. The Riemann zeta function is a function which encodes the behaviour of prime numbers. One of the main goals will be to give a detailed proof of the prime number theorem, which gives a precise estimate for the number of primes less than any large number.

The necessary background for this course will be Elementary Number Theory (Math 3461) and Analysis (series, sequences as given in Math 2570 and Math 3500). Some background in complex variables will be helpful but is not required for this course.
SPECIFIC TOPICS TO BE COVERED:

The main goals of this course are to prove the prime number theorem (with error term) and Dirichlet's theorem on primes in arithmetic progressions and to learn some of the main tools of analytic number theory.

In particular, some of the topics I plan to cover are:
ASSIGNMENTS AND EXAMS:
There will be regular homework assignments.
TEXTBOOK REFERENCES
There is no official textbook for this course. However, we shall make use of the following references.
Multiplicative number theory (3rd Edition) by H. Davenport.
Multiplicative Number Theory 1. Classical Theory by H.L. Montgomery and R.C. Vaughan.
Introduction to Analytic Number Theory by T.M. Apostol.
An introduction to the theory of numbers by Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery.

Links:
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Mathematics & Computer Science Department
University of Lethbridge