Abstract:Abstract. This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied but needs to be generalized first. Sometimes very satisfactory generalizations exist, while sometimes we have to make do with theories that have some of the desirable properties of Fourier analysis but not all of them. In the latter case, there are intriguing hints that there may be more satisfactory theories yet to be discovered. This article g… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.