Roth’s theorem in the primes

Ben Green

Type: Article

Publication Date: 2005-05-01

Citations: 164

DOI: https://doi.org/10.4007/annals.2005.161.1609

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.

Locations

Annals of Mathematics - View - PDF

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Works Cited by This (21)

Action	Title	Year	Authors
+	Integer sets containing no arithmetic progressions	1990	Endre Szemerédi
+	Multiplicative Number Theory	1980	H. Davenport
+	On Λ(p)-subsets of squares	1989	Jean Bourgain
+	On Triples in Arithmetic Progression	1999	Jean Bourgain
+	Counting sumsets and sum-free sets modulo a prime	2004	Ben Green Imre Z. Ruzsa
+ PDF Chat	Restriction and Kakeya phenomena for finite fields	2004	Gerd Mockenhaupt Terence Tao
+	On Sets of Integers Which Contain No Three Terms in Arithmetical Progression	1946	Felix Behrend
+ PDF Chat	Exponential sums over primes in an arithmetic progression	1985	Antal Balog Alberto Perelli
+	Integer Sets Containing No Arithmetic Progressions	1987	D. R. Heath‐Brown
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