Ben Green

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All published works

Action	Title	Year	Authors
+ PDF Chat	Improved bounds for the Furstenberg-S\'ark\"ozy theorem	2024	Ben Green Mehtaab Sawhney
+ PDF	Sumsets and entropy revisited	2024	Ben Green Freddie Manners Terence Tao
+ PDF Chat	Marton's Conjecture in abelian groups with bounded torsion	2024	W. T. Gowers Ben Green Freddie Manners Terence Tao
+ PDF	Equal sums in random sets and the concentration of divisors	2023	Kevin Ford Ben Green Dimitris Koukoulopoulos
+	Sumsets and entropy revisited	2023	Ben Green Freddie Manners Terence Tao
+	Waring's problem with restricted digits	2023	Ben Green
+	On a conjecture of Marton	2023	W. T. Gowers Ben Green Freddie Manners Terence Tao
+ PDF	New lower bounds for van der Waerden numbers	2022	Ben Green
+	On Sárközy's theorem for shifted primes	2022	Ben Green
+	A Weighted Prékopa–Leindler Inequality and Sumsets with Quasicubes	2022	Ben Green Dávid Matolcsi Imre Z. Ruzsa George Shakan Dmitrii Zhelezov
+ PDF	Lower bounds for corner-free sets	2021	Ben Green
+ PDF	Multiple correlation sequences not approximable by nilsequences	2021	Jop Briët Ben Green
+ PDF	Extremal problems for GCDs	2021	Ben Green Aled Walker
+	Lower bounds for corner-free sets	2021	Ben Green
+	Quadratic forms in 8 prime variables	2021	Ben Green
+	New lower bounds for van der Waerden numbers	2021	Ben Green
+ PDF	On a conjecture of Gowers and Long	2020	Ben Green
+ PDF Chat	On the width of transitive sets: Bounds on matrix coefficients of finite groups	2020	Ben Green
+	A Weighted Prékopa-Leindler inequality and sumsets with quasicubes	2020	Ben Green Dávid Matolcsi Imre Z. Ruzsa George Shakan Dmitrii Zhelezov
+	Multiple correlation sequences not approximable by nilsequences	2020	Jop Briët Ben Green
+	Equal sums in random sets and the concentration of divisors	2019	Kevin R. Ford Ben Green Dimitris Koukoulopoulos
+ PDF	On the arithmetic Kakeya conjecture of Katz and Tao	2018	Ben Green Imre Z. Ruzsa
+ PDF	An Example Concerning Set Addition in $$\mathbb{F}_2^n$$ F 2 n	2018	Ben Green Daniel M. Kane
+	Nonzero coefficients of half-integral weight modular forms mod $$\ell $$ ℓ	2018	Joël Bellaïche Ben Green K. Soundararajan
+ PDF	A note on multiplicative functions on progressions to large moduli	2017	Ben Green
+	Non-zero coefficients of half-integral weight modular forms mod $\ell$	2017	Joël Bellaïche Ben Green K. Soundararajan
+ PDF Chat	Invariable generation of the symmetric group	2017	Sean Eberhard Kevin Ford Ben Green
+	Long gaps between primes	2017	Kevin Ford Ben Green Sergeĭ Konyagin James Maynard Terence Tao
+	An example concerning set addition in F_2^n	2017	Ben Green Daniel M. Kane
+	New bounds for Szemerédi's theorem, III: A polylogarithmic bound for $r_4(N)$	2017	Ben Green Terence Tao
+	On the arithmetic Kakeya conjecture of Katz and Tao	2017	Ben Green Imre Z. Ruzsa
+ PDF	NEW BOUNDS FOR SZEMERÉDI'S THEOREM, III: A POLYLOGARITHMIC BOUND FOR	2017	Ben Green Terence Tao
+	Non-zero coefficients of half-integral weight modular forms mod $\ell$	2017	Joël Bellaïche Ben Green K. Soundararajan
+ PDF Chat	Sárközy's Theorem in Function Fields	2016	Ben Green
+ PDF Chat	On the Chromatic Number of Random Cayley Graphs	2016	Ben Green
+	Emmanuel Breuillard and Hee Oh, Thin groups and superstrong approximation (Cambridge University Press, 2014), 376 pp., 978-1-107-03685-7 (hardback), £65.	2016	Ben Green
+ PDF Chat	Large gaps between consecutive prime numbers	2016	Kevin Ford Ben Green Sergeĭ Konyagin Terence Tao
+ PDF	Monochromatic sums and products	2016	Ben Green Tom Sanders
+	A note on multiplicative functions on progressions to large moduli	2016	Ben Green
+	Sarkozy's theorem in function fields	2016	Ben Green
+	Monochromatic solutions to $x + y = z^2$	2016	Ben Green Sofia Lindqvist
+ PDF Chat	Permutations Fixing a<i>k</i>-set	2015	Sean Eberhard Kevin Ford Ben Green
+ PDF Chat	Counting sets with small sumset and applications	2015	Ben Green Robert Morris
+	Fourier uniformity on subspaces	2015	Ben Green Tom Sanders
+ PDF	Inverse questions for the large sieve	2014	Ben Green Adam J. Harper
+ PDF	Sets of integers with no large sum-free subset	2014	Sean Eberhard Ben Green Freddie Manners
+ PDF	On the quantitative distribution of polynomial nilsequences -- erratum	2014	Ben Green Terence Tao
+	Long gaps between primes	2014	Kevin Ford Ben Green Sergeĭ Konyagin James Maynard Terence Tao
+	Bounded gaps between primes	2014	Ben Green
+	Approximate algebraic structure	2014	Ben Green
+	Large gaps between consecutive prime numbers	2014	Kevin Ford Ben Green Sergeĭ Konyagin Terence Tao
+ PDF	On Sets Defining Few Ordinary Lines	2013	Ben Green Terence Tao
+ PDF Chat	Contractions and expansion	2013	Emmanuel Breuillard Ben Green
+	A nilpotent Freiman dimension lemma	2013	Emmanuel Breuillard Ben Green Terence Tao
+	Expansion in finite simple groups of Lie type	2013	Emmanuel Breuillard Ben Green Robert M. Guralnick Terence Tao
+	Small Doubling in Groups	2013	Emmanuel Breuillard Ben Green Terence Tao
+	Counting sets with small sumset and applications	2013	Ben Green Robert Morris
+	On the quantitative distribution of polynomial nilsequences - erratum	2013	Ben Green Terence Tao
+	Small doubling in groups	2013	Emmanuel Breuillard Ben Green Terence Tao
+ PDF Chat	The structure of approximate groups	2012	Emmanuel Breuillard Ben Green Terence Tao
+ PDF	An inverse theorem for the Gowers U^(s+1)[N]-norm	2012	Ben Green Terence Tao Tamar Ziegler
+	WHAT IS...an Approximate Group?	2012	Ben Green
+ PDF Chat	Strongly dense free subgroups of semisimple algebraic groups	2012	Emmanuel Breuillard Ben Green Robert M. Guralnick Terence Tao
+ PDF	The Möbius function is strongly orthogonal to nilsequences	2012	Ben Green Terence Tao
+ PDF	The quantitative behaviour of polynomial orbits on nilmanifolds	2012	Ben Green Terence Tao
+	New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited	2012	Ben Green Terence Tao
+ PDF	Approximate groups III: the unitary case	2012	Emmanuel Breuillard Ben Green
+	On sets defining few ordinary lines	2012	Ben Green Terence Tao
+	Simply-laced isomonodromy systems . On the functions counting walks with small steps in the quarter plane . The structure of approximate groups . On stably free modules over affine algebras . Perfectoid spaces	2012	Philip Boalch Irina Kurkova Kilian Raschel Emmanuel Breuillard Ben Green Terence Tao Jean Fasel Ravi A. Rao Richard G. Swan Peter Scholze
+ PDF Chat	Approximate Subgroups of Linear Groups	2011	Emmanuel Breuillard Ben Green Terence Tao
+ PDF	An inverse theorem for the Gowers $U^{s+1}[N]$-norm	2011	Tamar Ziegler Terence Tao Ben Green
+	A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups	2011	Emmanuel Breuillard Ben Green Terence Tao
+	The structure of approximate groups	2011	Emmanuel Breuillard Ben Green Terence Tao
+	Contractions and expansion	2011	Emmanuel Breuillard Ben Green
+	On (not) computing the Mobius function using bounded depth circuits	2011	Ben Green
+	A nilpotent Freiman dimension lemma	2011	Emmanuel Breuillard Ben Green Terence Tao
+	III.92 Trigonometric Functions	2010	Ben Green
+	III.58 Modular Arithmetic	2010	Ben Green
+	III.41 Irrational and Transcendental Numbers	2010	Ben Green
+ PDF	Linear approximate groups	2010	Emmanuel Breuillard Ben Green Terence Tao
+ PDF	AN INVERSE THEOREM FOR THE GOWERS<i>U</i><sup>4</sup>-NORM	2010	Ben Green Terence Tao Tamar Ziegler
+	Approximate groups. I The torsion-free nilpotent case	2010	Emmanuel Breuillard Ben Green
+ PDF Chat	An equivalence between inverse sumset theorems and inverse conjectures for the<i>U</i><sup>3</sup>norm	2010	Ben Green Terence Tao
+	A Note on Elkin’s Improvement of Behrend’s Construction	2010	Ben Green Julia Wolf
+	An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement)	2010	Ben Green Terence Tao Tamar Ziegler
+ PDF Chat	Yet Another Proof Of Szemerédi's Theorem	2010	Ben Green Terence Tao
+	Linear Approximate Groups	2010	Emmanuel Breuillard Ben Green Terence Tao
+	Suzuki groups as expanders	2010	Emmanuel Breuillard Ben Green Terence Tao
+ PDF Chat	An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications	2010	Ben Green Terence Tao
+	An inverse theorem for the Gowers U^{s+1}[N]-norm	2010	Ben Green Terence Tao Tamar Ziegler
+	Strongly dense free subgroups of semisimple algebraic groups	2010	Emmanuel Breuillard Ben Green Robert M. Guralnick Terence Tao
+	Approximate subgroups of linear groups	2010	Emmanuel Breuillard Ben Green Terence Tao
+	Approximate groups, III: the unitary case	2010	Emmanuel BREUILLAND Emmanuel Breuillard Ben Green
+	An arithmetic regularity lemma, associated counting lemma, and applications	2010	Ben Green Terence Tao
+ PDF Chat	A note on Elkin's improvement of Behrend's construction	2010	Ben Green Julia Wolf
+	Yet another proof of Szemeredi's theorem	2010	Ben Green Terence Tao
+ PDF Chat	Freiman's Theorem in Finite Fields via Extremal Set Theory	2009	Ben Green Terence Tao
+ PDF	A NOTE ON THE FREIMAN AND BALOG–SZEMERÉDI–GOWERS THEOREMS IN FINITE FIELDS	2009	Benjamin Green Terence Tao
+ PDF	On the Littlewood Problem Modulo a Prime	2009	Ben Green Sergeĭ Konyagin
+	Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak	2009	Ben Green
+	Sum-product phenomena in F_p: a brief introduction	2009	Ben Green
+	Approximate groups, I: the torsion-free nilpotent case	2009	Emmanuel Breuillard Ben Green
+	Approximate groups, II: the solvable linear case	2009	Emmanuel Breuillard Ben Green
+ PDF Chat	On the maximal number of 3-term arithmetic progressions in subsets of ℤ/<i>p</i> ℤ	2008	Ben Green Olof Sisask
+	On a variant of the large sieve	2008	Ben Green
+ PDF Chat	New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries	2008	Ben Green Terence Tao
+	The Mobius and Nilsequences Conjecture	2008	Ben Green Terence Tao
+ PDF Chat	Boolean Functions with small Spectral Norm	2008	Ben Green Tom Sanders
+ PDF	AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM	2008	Ben Green Terence Tao
+ PDF	Quadratic uniformity of the Möbius function	2008	Ben Green Terence Tao
+	On a variant of the large sieve	2008	Ben Green
+	Montréal notes on quadratic Fourier analysis	2007	Ben Green
+ PDF Chat	Freiman's theorem in an arbitrary abelian group	2007	Ben Green Imre Z. Ruzsa
+	The distribution of polynomials over finite fields, with applications to the Gowers norms	2007	Ben Green Terence Tao
+ PDF	Three Topics in Additive Prime Number Theory	2007	Ben Green
+	The quantitative behaviour of polynomial orbits on nilmanifolds	2007	Ben Green Terence Tao
+	Three topics in additive prime number theory	2007	Ben Green
+	Freiman's theorem in finite fields via extremal set theory	2007	Ben Green Terence Tao
+	A note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields	2007	Ben Green Terence Tao
+ PDF Chat	SETS WITH SMALL SUMSET AND RECTIFICATION	2006	Ben Green Imre Z. Ruzsa
+	SETS WITH SMALL SUMSET AND RECTIFICATION	2006	Ben Green Imre Z. Ruzsa
+	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
+ PDF	Restriction theory of the Selberg sieve, with applications	2006	Ben Green Terence Tao
+	On the Littlewood problem modulo a prime	2006	Ben Green Sergeĭ Konyagin
+	Quadratic Uniformity of the Mobius Function	2006	Ben Green Terence Tao
+	Linear Equations in Primes	2006	Ben Green Terence Tao
+ PDF Chat	Sum-free sets in abelian groups	2005	Ben Green Imre Z. Ruzsa
+	Finite field models in additive combinatorics	2005	Ben Green
+ PDF Chat	Counting Sets With Small Sumset, And The Clique Number Of Random Cayley Graphs	2005	Ben Green
+	Set addition in boxes and the Freiman-Bilu theorem	2005	Ben Green
+	Long arithmetic progressions of primes	2005	Ben Green
+	An inverse theorem for the Gowers U^3 norm	2005	Ben Green Terence Tao
+	Freiman's Theorem in an arbitrary abelian group	2005	Ben Green Imre Z. Ruzsa
+	Compressions, convex geometry and the Freiman-Bilu theorem	2005	Ben Green Terence Tao
+ PDF Chat	On the Hardy–Littlewood majorant problem	2004	Ben Green Imre Z. Ruzsa
+ PDF Chat	THE CAMERON–ERDOS CONJECTURE	2004	Ben Green
+	Counting sumsets and sum-free sets modulo a prime	2004	Ben Green Imre Z. Ruzsa
+	Spectral Structure of Sets of Integers	2004	Ben Green
+	Restriction theory of the Selberg sieve, with applications	2004	Ben Green Terence Tao
+	Finite field models in additive combinatorics	2004	Ben Green
+	The primes contain arbitrarily long arithmetic progressions	2004	Ben Green Terence Tao
+	Sets with small sumset and rectification	2004	Ben Green Imre Z. Ruzsa
+	A Szemeredi-type regularity lemma in abelian groups	2003	Ben Green
+	Some Constructions in the Inverse Spectral Theory of Cyclic Groups	2003	Ben Green
+	Roth's theorem in the primes	2003	Ben Green
+	A Szemeredi-type regularity lemma in abelian groups, with applications	2003	Ben Green
+	The Cameron-Erdos Conjecture	2003	Ben Green
+	Sum-free sets in abelian groups	2003	Ben Green Imre Z. Ruzsa
+	Counting sets with small sumset, and the clique number of random Cayley graphs	2003	Ben Green
+	Roth's theorem in the primes	2003	Ben Green
+ PDF	On arithmetic structures in dense sets of integers	2002	Ben Green
+ PDF	The number of squares and B<sub>h</sub>[g] sets	2001	Ben Green

Common Coauthors

Coauthor	Papers Together
Terence Tao	61
Emmanuel Breuillard	23
Imre Z. Ruzsa	13
Kevin Ford	7
Sergeĭ Konyagin	6
Freddie Manners	5
Tamar Ziegler	5
K. Soundararajan	3
Sean Eberhard	3
Robert M. Guralnick	3
Tom Sanders	3
Joël Bellaïche	3
W. T. Gowers	2
Dimitris Koukoulopoulos	2
Daniel M. Kane	2
Jop Briët	2
James Maynard	2
Julia Wolf	2
Dávid Matolcsi	2
Dmitrii Zhelezov	2
Robert Morris	2
George Shakan	2
Kilian Raschel	1
Aled Walker	1
Olof Sisask	1
Philip Boalch	1
Sofia Lindqvist	1
Adam J. Harper	1
Richard G. Swan	1
Peter Scholze	1
Emmanuel BREUILLAND	1
Kevin R. Ford	1
Ravi A. Rao	1
Mehtaab Sawhney	1
Irina Kurkova	1
Jean Fasel	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four	1998	W. T. Gowers	38
+	On Triples in Arithmetic Progression	1999	Jean Bourgain	23
+ PDF	The primes contain arbitrarily long arithmetic progressions	2008	Benjamin Green Terence Tao	22
+ PDF	AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM	2008	Ben Green Terence Tao	20
+	Additive Combinatorics	2006	Terence Tao Van H. Vu	20
+	A polynomial bound in Freiman's theorem	2002	Mei-Chu Chang	19
+	Generalized arithmetical progressions and sumsets	1994	Imre Z. Ruzsa	17
+ PDF Chat	Freiman's theorem in an arbitrary abelian group	2007	Ben Green Imre Z. Ruzsa	17
+	On Certain Sets of Integers	1953	K. F. Roth	16
+	A statistical theorem of set addition	1994	Antal Balog Endre Szemer�di	15
+ PDF Chat	Product set estimates for non-commutative groups	2008	Terence Tao	15
+	A new proof of Szemerédi's theorem	2001	W. T. Gowers	15
+ PDF	The quantitative behaviour of polynomial orbits on nilmanifolds	2012	Ben Green Terence Tao	14
+ PDF	Multiple recurrence and nilsequences	2005	Vitaly Bergelson Bernard Host Bryna Kra Imre Z. Ruzsa	14
+	Polynomial Sequences in Groups	1998	A. Leibman	13
+	Universal characteristic factors and Furstenberg averages	2006	Tamar Ziegler	13
+ PDF Chat	Low-degree tests at large distances	2007	Alex Samorodnitsky	12
+ PDF	Linear equations in primes	2010	Ben Green Terence Tao	12
+ PDF	Nonconventional ergodic averages and nilmanifolds	2005	Bernard Host Bryna Kra	12
+	Groups of polynomial growth and expanding maps	1981	Mikhael Gromov	11
+	Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions	1977	Harry Furstenberg	11
+	Quasirandom Groups	2008	W. T. Gowers	11
+	Integer Sets Containing No Arithmetic Progressions	1987	D. R. Heath‐Brown	10
+ PDF Chat	Approximate Subgroups of Linear Groups	2011	Emmanuel Breuillard Ben Green Terence Tao	10
+	Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold	2004	A. Leibman	10
+ PDF Chat	An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications	2010	Ben Green Terence Tao	10
+	Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis	1994	Hugh L. Montgomery	10
+	An Application of Graph Theory to Additive Number Theory	1985	Noga Alon P. Erdős	10
+	Finite subgroups of algebraic groups	2011	Michael Larsen Richard Pink	10
+	Stable group theory and approximate subgroups	2009	Ehud Hrushovski	9
+	Free subgroups in linear groups	1972	Jacques Tits	9
+ PDF	Sur les groupes nilpotents et les anneaux de Lie	1954	Michel Lazard	9
+	Freiman's theorem for solvable groups	2010	Terence Tao	9
+ PDF Chat	APPROXIMATE GROUPS, II: THE SOLVABLE LINEAR CASE	2010	Emmanuel Breuillard B. Green	9
+ PDF Chat	Generalising the Hardy–Littlewood method for primes	2007	Ben J. Green	8
+	Linear equations in primes	1992	Antal Balog	8
+ PDF	Growth and generation in SL<sub>2</sub>(ℤ∕pℤ)	2008	H. A. Helfgott	8
+	Uniform Distribution of Generalized Polynomials	1993	Inger Johanne Håland	8
+ PDF	Quadratic uniformity of the Möbius function	2008	Ben Green Terence Tao	8
+	Finite field models in additive combinatorics	2005	Ben Green	8
+ PDF	On sets of integers containing k elements in arithmetic progression	1975	Endre Szemerédi	8
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	8
+	Convergence of Conze–Lesigne averages	2001	Bernard Host Bryna Kra	7
+	Multiplicative Number Theory	1980	H. Davenport	7
+ PDF	Uniform expansion bounds for Cayley graphs of SL<sub>2</sub>(𝔽<sub>p</sub>)	2008	Jean Bourgain Alex Gamburd	7
+	Arithmetic progressions in sumsets	2002	B. Green	7
+ PDF	A Finitary Version of Gromov’s Polynomial Growth Theorem	2010	Yehuda Shalom Terence Tao	7
+ PDF	Distribution of values of bounded generalized polynomials	2007	Vitaly Bergelson A. Leibman	7
+	On Certain Sets of Positive Density	1959	P. Varnavides	7
+ PDF	Roth’s theorem in the primes	2005	Ben Green	7