On the hardy-littlewood majorant problem

Ben Green, Imre Z. Ruzsa

Research output: Contribution to journalArticle

7 Citations (Scopus)


Let A ⊆ {1,..., N} and let {a n} n∈Λ be a sequence with \a n\ ≤ 1 for all n. It is easy to see that || n∈Λ∑a ne(nθ)|| p≤|| n∈Λ∑e(nθ)|| p for every even integer p. We give an example which shows that this statement can fail rather dramatically when p is not an even integer. This answers in the negative a question known as the Hardy-Littlewood majorant conjecture, thereby ruling out a certain approach to the restriction and Kakeya families of conjectures.

Original languageEnglish
Pages (from-to)511-517
Number of pages7
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
Publication statusPublished - Nov 1 2004


ASJC Scopus subject areas

  • Mathematics(all)

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