Yet Another Proof Of Szemerédi's Theorem

Ben Green, Terence Tao

Type: Book-Chapter

Publication Date: 2010-01-01

Citations: 9

DOI: https://doi.org/10.1007/978-3-642-14444-8_8

Abstract

To Endre Szemerédi on the occasion of his 70th birthday Using the density-increment strategy of Roth and Gowers, we derive Szemerédi’s theorem on arithmetic progressions from the inverse conjectures GI (s) for the Gowers norms, recently established by the authors and Ziegler in [8].

Locations

Bolyai Society mathematical studies - View
arXiv (Cornell University) - PDF
arXiv (Cornell University) - View - PDF
Bolyai Society mathematical studies - View
arXiv (Cornell University) - PDF
arXiv (Cornell University) - View - PDF
Bolyai Society mathematical studies - View
arXiv (Cornell University) - PDF
arXiv (Cornell University) - View - PDF

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Action	Title	Year	Authors
+ PDF Chat	Gowers norms control diophantine inequalities	2020	Aled Walker
+ PDF Chat	Diophantine equations in the primes	2014	Brian Cook Ákos Magyar
+ PDF	Generalizations of Fourier analysis, and how to apply them	2016	W. T. Gowers
+	Distinct distances and arithmetic progressions	2017	Adrian Dumitrescu
+ PDF Chat	Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition	2013	Khodakhast Bibak
+	Coloring and extremal problems in combinatorics	2010	Jacob Manske
+	A Model Theoretic Proof of Szemerédi's Theorem	2010	Henry Towsner
+	Arithmetic Progressions and Ergodic Theory	2015	Tanja Eisner Bálint Farkas Markus Haase Rainer Nagel
+	Recurrence and non-uniformity of bracket polynomials	2013	Matthew Tointon

Works Cited by This (10)

Action	Title	Year	Authors
+ PDF	On sets of integers containing k elements in arithmetic progression	1975	Endre Szemerédi
+ PDF	AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM	2008	Ben Green Terence Tao
+	An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement)	2010	Ben Green Terence Tao Tamar Ziegler
+	On Certain Sets of Integers	1953	K. F. Roth
+	The quantitative behaviour of polynomial orbits on nilmanifolds	2007	Ben Green Terence Tao
+	On sets of integers containing no four elements in arithmetic progression	1969	Endre Szemerédi
+	A new proof of Szemerédi's theorem	2001	W. T. Gowers
+	A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four	1998	W. T. Gowers
+ PDF	AN INVERSE THEOREM FOR THE GOWERS<i>U</i><sup>4</sup>-NORM	2010	Ben Green Terence Tao Tamar Ziegler
+ PDF Chat	Coherence measures for heralded single-photon sources	2009	Erwann Bocquillon Christophe Couteau Mohsen Razavi Raymond Laflamme Gregor Weihs