New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited

Ben Green, Terence Tao

Type: Preprint

Publication Date: 2012-01-01

Citations: 7

DOI: https://doi.org/10.48550/arxiv.1205.1330

View Publication

Locations

arXiv (Cornell University) - View
DataCite API - View
arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries	2008	Ben Green Terence Tao
+	New bounds for Szemeredi's theorem, II: A new bound for $r_4(N)$	2006	Ben Green Terence Tao
+	New bounds for Szemerédi's theorem, III: A polylogarithmic bound for $r_4(N)$	2017	Ben Green Terence Tao
+ PDF Chat	Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields	2024	Christian Elsholtz Zach Hunter Laura Proske Lisa Sauermann
+ PDF	NEW BOUNDS FOR SZEMERÉDI'S THEOREM, III: A POLYLOGARITHMIC BOUND FOR	2017	Ben Green Terence Tao
+	Sets without $k$-term progressions can have many shorter progressions	2019	Jacob Fox Cosmin Pohoata
+	Sets without $k$-term progressions can have many shorter progressions	2019	Jacob Fox Cosmin Pohoata
+	Further bounds in the polynomial Szemerédi theorem over finite fields	2019	Borys Kuca
+ PDF	Sets without <i>k</i>‐term progressions can have many shorter progressions	2020	Jacob Fox Cosmin Pohoata
+	A Constructive Lower Bound on Szemerédi's Theorem	2017	Vladislav Taranchuk
+	Caps and progression-free sets in $\mathbb{Z}_m^n$	2019	Christian Elsholtz Péter Pál Pach
+	Caps and progression-free sets in $\mathbb{Z}_m^n$	2019	Christian Elsholtz Péter Pál Pach
+	A generalization of sets without long arithmetic progressions based on Szekeres algorithm	2013	Xiaodong Xu
+ PDF Chat	ON A GENERALIZATION OF SZEMERÉDI'S THEOREM	2006	Ilya D. Shkredov
+	Further bounds in the polynomial Szemer	2021	Borys Kuca
+	Asymptotic upper bounds on progression-free sets in $\mathbb{Z}_p^n$	2016	Dion Gijswijt
+	On a Generalization of Szemeredi's Theorem	2005	Ilya D. Shkredov
+ PDF	Progression-free sets in $\mathbb{Z}_4^n$ are exponentially small	2016	Ernie Croot Vsevolod F. Lev Péter Pál Pach
+	A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four	1998	W. T. Gowers
+	Szemerédi's theorem and problems on arithmetic progressions	2006	Ilya D. Shkredov

Works That Cite This (7)

Action	Title	Year	Authors
+ PDF	On Arithmetic Progressions in Symmetric Sets in Finite Field Model	2020	Jan Hązła
+ PDF	NEW BOUNDS FOR SZEMERÉDI'S THEOREM, III: A POLYLOGARITHMIC BOUND FOR	2017	Ben Green Terence Tao
+ PDF	Finite field models in arithmetic combinatorics – ten years on	2014	Jason B. Wolf
+ PDF Chat	Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition	2013	Khodakhast Bibak
+	Popular progression differences in vector spaces	2017	Jacob Fox Huy Tuan Pham
+	Caps and progression-free sets in $\mathbb{Z}_m^n$	2019	Christian Elsholtz Péter Pál Pach
+ PDF	Finding solutions with distinct variables to systems of linear equations over $$\mathbb {F}_p$$	2022	Lisa Sauermann

Works Cited by This (14)

Action	Title	Year	Authors
+ PDF	AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM	2008	Ben Green Terence Tao
+	New bounds for Szemeredi's theorem, II: A new bound for $r_4(N)$	2006	Ben Green Terence Tao
+	Montreal Lecture Notes on Quadratic Fourier Analysis	2006	Ben Green
+	New Bounds on cap sets	2011	Michael Bateman Nets Hawk Katz
+	Integer Sets Containing No Arithmetic Progressions	1987	D. R. Heath‐Brown
+	A density version of the Hales-Jewett theorem	1991	Hillel Fürstenberg Yitzhak Katznelson
+ PDF Chat	An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications	2010	Ben Green Terence Tao
+	The inverse conjecture for the Gowers norm over finite fields in low characteristic	2011	Terence Tao Tamar Ziegler
+	An inverse theorem for the Gowers U^3 norm	2005	Ben Green Terence Tao
+	Finite field models in additive combinatorics	2004	Ben Green