**Graduate Studies in Mathematics**

Volume: 142;
2012;
187 pp;
Hardcover

MSC: Primary 11; 37;

Print ISBN: 978-0-8218-8986-2

Product Code: GSM/142

List Price: $54.00

Individual Member Price: $43.20

**Electronic ISBN: 978-0-8218-9194-0
Product Code: GSM/142.E**

List Price: $54.00

Individual Member Price: $43.20

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#### Supplemental Materials

# Higher Order Fourier Analysis

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*Terence Tao*

Traditional Fourier analysis, which has been
remarkably effective in many contexts, uses linear phase functions to
study functions. Some questions, such as problems involving
arithmetic progressions, naturally lead to the use of quadratic or
higher order phases. Higher order Fourier analysis is a subject that
has become very active only recently. Gowers, in groundbreaking work,
developed many of the basic concepts of this theory in order to give a
new, quantitative proof of Szemerédi's theorem on arithmetic
progressions. However, there are also precursors to this theory in
Weyl's classical theory of equidistribution, as well as in
Furstenberg's structural theory of dynamical systems.

This book, which is the first monograph in this area, aims to cover
all of these topics in a unified manner, as well as to survey some of
the most recent developments, such as the application of the theory to
count linear patterns in primes. The book serves as an introduction
to the field, giving the beginning graduate student in the subject a
high-level overview of the field. The text focuses on the simplest
illustrative examples of key results, serving as a companion to the
existing literature on the subject. There are numerous exercises with
which to test one's knowledge.

#### Table of Contents

# Table of Contents

## Higher Order Fourier Analysis

#### Readership

Graduate students and research mathematicians interested in harmonic analysis and number theory.