Last updated: Feb 24, 2013
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 ???: 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 Pavel Zorin for corrections.