English

Montreal Lecture Notes on Quadratic Fourier Analysis

Classical Analysis and ODEs 2007-05-23 v2 Combinatorics

Abstract

These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand it at the present time. Specifically, we will describe ``quadratic objects'' of various types and their relation to additive structures, particularly four-term arithmetic progressions. I will focus on qualitative results, referring the reader to the literature for the many interesting quantitative questions in this theory. Thus these lectures have a distinctly ``soft'' flavour in many places. Some of the notes cover unpublished work which is joint with Terence Tao. This will be published more formally at some future juncture.

Keywords

Cite

@article{arxiv.math/0604089,
  title  = {Montreal Lecture Notes on Quadratic Fourier Analysis},
  author = {Ben Green},
  journal= {arXiv preprint arXiv:math/0604089},
  year   = {2007}
}

Comments

34 pages. To be published in Proceedings of the CRM-Clay Conference on Additive Combinatorics, Montreal 2006

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