On the hardy-littlewood majorant problem

Ben Green, I. Ruzsa

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume137
Issue number3
DOIs
Publication statusPublished - Nov 2004

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Cite this

On the hardy-littlewood majorant problem. / Green, Ben; Ruzsa, I.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 137, No. 3, 11.2004, p. 511-517.

Research output: Contribution to journalArticle

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