Last updated: Jan 10, 2014
Higher order Fourier analysis
Graduate Studies in Mathematics, 142
American Mathematical Society, 2012
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“.
- Page 98: In the definition of a nilpotent filtered group , the additional hypothesis that is also nilpotent is required (this is automatic in the most important case , but not in general).
- Page 100: In the first paragraph, replace “starting from a point” with “starting with the base group , which is a point in the most important case “. Similarly, after Exercise 1.6.14, replace “starting from a point” by “starting from the base space , which is a point in the most important case “.
- Page 109: In Exercise 1.6.22, the argument indicated only works under the stronger hypothesis that 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 Ben Green and Pavel Zorin for corrections.