Last updated: Feb 24, 2013

Higher order Fourier analysis
Terence Tao

Graduate Studies in Mathematics, 142

American Mathematical Society, 2012

ISBN-10: 0-8218-8986-9
ISBN-13: 978-0-8218-8986-2

This continues my series of books derived from my blog. The preceding books in this series were “Structure and Randomness“, “Poincaré’s legacies“, “An epsilon of room“, “An introduction to measure theory“, and “Topics in random matrix theory“.

An online version of the text can be found here.  It is based primarily on these lecture notes.

Errata:

• Page ???: In Exercise 1.6.22, the argument indicated only works under the stronger hypothesis that $\alpha, \beta, \alpha \beta$ are linearly independent modulo 1 over the integers.  (To handle the general case, one either needs the more complicated quantitative (single-scale) relative van der Corput lemma in my paper with Green, or else rely on the ergodic theorem as was done in the paper of Leibman.)

Thanks to Pavel Zorin for corrections.