On arithmetic structures in dense sets of integers

BJ Green

Research output: Contribution to journalArticle (Academic Journal)peer-review

30 Citations (Scopus)


We prove that if A subset of or equal to {1,...,N} has density at least (log log N)(-c), where c is an absolute constant, then A contains a triple (a, a+ d, a +2d) with d = x(2)+y(2) for some integers x, y, not both zero. We combine methods of T Gowers and A. Sarkozy with an application of Selberg's sieve. The result may be regarded as a step toward establishing a fully quantitative version of the polynomial Szemeridi theorem of V. Bergelson and A. Leibman.
Translated title of the contributionOn arithmetic structures in dense sets of integers
Original languageEnglish
Pages (from-to)215 - 238
JournalDuke Mathematical Journal
Volume114 (2)
Publication statusPublished - Aug 2002

Bibliographical note

Publisher: Duke Univ Press
Other identifier: IDS Number: 589UA


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