Roth's theorem in the primes

BJ Green

Roth's theorem in the primes

BJ Green

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

103 Citations (Scopus)

Abstract

We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes.

Translated title of the contribution	Roth's theorem in the primes
Original language	English
Pages (from-to)	1609 - 1636
Journal	Annals of Mathematics
Volume	161 (3)
Publication status	Published - May 2005

Bibliographical note

Publisher: Ann Mathematics
Other identifier: IDS Number: 980YR

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title = "Roth's theorem in the primes",

abstract = "We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes.",

author = "BJ Green",

note = "Publisher: Ann Mathematics Other identifier: IDS Number: 980YR ",

year = "2005",

month = may,

language = "English",

volume = "161 (3)",

pages = "1609 -- 1636",

journal = "Annals of Mathematics",

issn = "1939-8980",

publisher = "Princeton University Press",

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T1 - Roth's theorem in the primes

AU - Green, BJ

N1 - Publisher: Ann Mathematics Other identifier: IDS Number: 980YR

PY - 2005/5

Y1 - 2005/5

N2 - We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes.

AB - We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes.

M3 - Article (Academic Journal)

SN - 1939-8980

VL - 161 (3)

SP - 1609

EP - 1636

JO - Annals of Mathematics

JF - Annals of Mathematics

ER -

Roth's theorem in the primes

Abstract

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