Tomasz Schoen

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All published works

Action	Title	Year	Authors
+	Translation-Invariant Equations With at Least Four Variables	2024	Tomasz Schoen
+ PDF Chat	Note on the Theorem of Balog, Szemerédi, and Gowers	2024	Christian Reiher Tomasz Schoen
+	Note on the Theorem of Balog, Szemerédi, and Gowers	2023	Christian Reiher Tomasz Schoen
+	On convex equations	2023	Tomasz Schoen
+	New bounds in the Bogolyubov-Ruzsa lemma	2023	Tomasz Kosciuszko Tomasz Schoen
+	A note on bilinear exponential sums in prime fields	2022	Tomasz Schoen
+ PDF Chat	Character sums estimates and an application to a problem of Balog	2022	Tomasz Schoen Ilya D. Shkredov
+	On Sumsets of Subsets of Squares	2021	Tomasz Schoen
+ PDF Chat	A Subexponential Upper Bound for van der Waerden Numbers $W(3,k)$	2021	Tomasz Schoen
+ PDF Chat	Improved bound in Roth's theorem on arithmetic progressions	2021	Tomasz Schoen
+	A Diophantine Ramsey Theorem	2020	Tomasz Schoen
+ PDF Chat	L-functions and sum-free sets	2020	Tomasz Schoen Ilya D. Shkredov
+	A subexponential upper bound for van der Waerden numbers W(3,k)	2020	Tomasz Schoen
+	Improved bound in Roth's theorem on arithmetic progressions	2020	Tomasz Schoen
+	$L$--functions and sum--free sets	2020	Tomasz Schoen Ilya D. Shkredov
+	A subexponential upper bound for van der Waerden numbers W(3,k)	2020	Tomasz Schoen
+	Improved bound in Roth's theorem on arithmetic progressions	2020	Tomasz Schoen
+	Character sums estimates and an application to a problem of Balog	2020	Tomasz Schoen Ilya D. Shkredov
+	$L$--functions and sum--free sets	2020	Tomasz Schoen Ilya D. Shkredov
+	An Upper Bound for Weak $B_k$-Sets	2019	Tomasz Schoen Ilya D. Shkredov
+ PDF Chat	Alternative approach to sums of dilates	2018	Rafał Bystrzycki Tomasz Schoen
+	Tight bounds on additive Ramsey-type numbers	2017	Karol Cwalina Tomasz Schoen
+	A remark on A+B and A-A for compact sets in R^n	2016	Tomasz Schoen Ilya D. Shkredov
+	An upper bound for weak $B_k$-sets	2016	Tomasz Schoen Ilya D. Shkredov
+ PDF Chat	ROTH’S THEOREM FOR FOUR VARIABLES AND ADDITIVE STRUCTURES IN SUMS OF SPARSE SETS	2016	Tomasz Schoen Olof Sisask
+	A Remark on A+B and A-A for Compact Sets in Rn.	2016	Tomasz Schoen Ilya D. Shkredov
+	A remark on A+B and A-A for compact sets in R^n	2016	Tomasz Schoen Ilya D. Shkredov
+ PDF Chat	ADDITIVE DIMENSION AND A THEOREM OF SANDERS	2015	Tomasz Schoen Ilya D. Shkredov
+	New bounds in Balog-Szemerédi-Gowers theorem	2014	Tomasz Schoen
+	Roth's theorem for four variables and additive structures in sums of sparse sets	2014	Tomasz Schoen Olof Sisask
+	Roth's theorem for four variables and additive structures in sums of sparse sets	2014	Tomasz Schoen Olof Sisask
+ PDF Chat	On Convolutions of Convex Sets and Related Problems	2013	Tomasz Schoen
+ PDF Chat	Roth’s theorem in many variables	2013	Tomasz Schoen Ilya D. Shkredov
+	Finding large co-Sidon subsets in sets with a given additive energy	2013	Artūras Dubickas Tomasz Schoen Manuel Silva Paulius Šarka
+	Higher moments of convolutions	2012	Tomasz Schoen Ilya D. Shkredov
+	A linear bound on the dimension in Green–Ruzsaʼs theorem	2012	Karol Cwalina Tomasz Schoen
+ PDF Chat	Arithmetic progressions in sparse sumsets	2012	Ernie Croot Imre Z. Ruzsa Tomasz Schoen
+	Linear equations and sets of integers	2012	Tomasz Schoen
+ PDF Chat	The number of solutions of a homogeneous linear congruence	2012	Karol Cwalina Tomasz Schoen
+	Higher moments of convolutions	2011	Tomasz Schoen Ilya D. Shkredov
+	On Sumsets of Convex Sets	2011	Tomasz Schoen Ilya D. Shkredov
+	Roth's theorem in many variables	2011	Tomasz Schoen Ilya D. Shkredov
+	On sumsets of convex sets	2011	Tomasz Schoen Ilya D. Shkredov
+	Near optimal bounds in Freiman's theorem	2011	Tomasz Schoen
+	ADDITIVE PROPERTIES OF MULTIPLICATIVE SUBGROUPS OF Fp	2011	Tomasz Schoen Ilya D. Shkredov
+ PDF Chat	Arithmetic progressions in sums of subsets of sparse sets	2011	Tomasz Schoen
+	Higher moments of convolutions	2011	Tomasz Schoen Ilya D. Shkredov
+	Roth's theorem in many variables	2011	Tomasz Schoen Ilya D. Shkredov
+	On sumsets of convex sets	2011	Tomasz Schoen Ilya D. Shkredov
+	Sum-intersective sets	2010	Tomasz Schoen
+	On a question of Cochrane and Pinner concerning multiplicative subgroups	2010	Tomasz Schoen Ilya D. Shkredov
+	Dense minimal asymptotic bases of order two	2009	Mirosława Jańczak Tomasz Schoen
+ PDF Chat	On sumsets and spectral gaps	2008	Ernie Croot Tomasz Schoen
+ PDF Chat	On a problem of Konyagin	2008	Tomasz Łuczak Tomasz Schoen
+	Difference Covers	2007	Tomasz Schoen
+ PDF Chat	Integer Sets Having the Maximum Number of Distinct Differences	2007	Oleg Pikhurko Tomasz Schoen
+	On Sumsets and Spectral Gaps	2007	Ernie Croot Tomasz Schoen
+	LINEAR EQUATIONS IN $\mathbb{Z}_{\lowercase{p}}$	2005	Tomasz Schoen
+	Squarefree numbers in sumsets	2005	Tomasz Schoen
+ PDF Chat	The Structure of Maximum Subsets of $\{1,\ldots,n\}$ with No Solutions to $a+b = kc$	2005	Andreas Baltz Peter Hegarty Jonas Knape Urban Larsson Tomasz Schoen
+	A note on unique representation bases for the integers	2004	Tomasz Łuczak Tomasz Schoen
+	Solution-free sets for linear equations	2003	Tomasz Łuczak Tomasz Schoen
+	On the discrepancy of combinatorial rectangles	2002	Noga Alon Benjamin Doerr Tomasz Łuczak Tomasz Schoen
+	The Cardinality of Restricted Sumsets	2002	Tomasz Schoen
+	The distribution of dense Sidon subsets of $ \mathbb{Z}_m $	2002	Tomasz Schoen
+	The Cardinality of Restricted Sumsets	2002	Tomasz Schoen
+	Cameron-Erdős Modulo a Prime	2002	Vsevolod F. Lev Tomasz Schoen
+	Sum-free sets in abelian groups	2001	Vsevolod F. Lev Tomasz Łuczak Tomasz Schoen
+	Sum-Free Subsets of Right Cancellative Semigroups	2001	Tomasz Łuczak Tomasz Schoen
+	On a Problem of Erdős and Sárközy	2001	Tomasz Schoen
+	Coloring t-dimensional m-Boxes	2001	Geir Agnarsson Benjamin Doerr Tomasz Schoen
+ PDF Chat	The number of (2,3)-sum-free subsets of { 1,...,n}	2001	Tomasz Schoen
+	On the number of maximal sum-free sets	2000	Tomasz Łuczak Tomasz Schoen
+	On the density of sets containing no three distinct numbers with all their sums	2000	Tomasz Schoen
+ PDF Chat	A Note on the Number of $(k,l)$-Sum-Free Sets	2000	Tomasz Schoen
+	A note on the number of -sum-free sets.	2000	Tomasz Schoen
+ PDF Chat	On the maximal density of sum-free sets	2000	Tomasz Łuczak Tomasz Schoen
+ PDF Chat	On sets of natural numbers without solution to a noninvariant linear equation	2000	Tomasz Schoen
+	On Sets of Natural Numbers Whose Sumset is Free of Squares	1999	Tomasz Schoen
+	The Number of Monochromatic Schur Triples	1999	Tomasz Schoen
+	On the Density of Universal Sum-Free Sets	1999	Tomasz Schoen
+	Probabilistic Construction of Small Strongly Sum-Free Sets via Large Sidon Sets	1999	Andreas Baltz Tomasz Schoen Anand Srivastav
+	Independent finite sums in graphs defined on the natural numbers	1998	Tomasz Łuczak Vojtěch Rödl Tomasz Schoen
+ PDF Chat	Small bases for finite groups	1998	Tomasz Łuczak Tomasz Schoen
+	On Infinite Sum-free Sets of Natural Numbers	1997	Tomasz Łuczak Tomasz Schoen
+ PDF Chat	On strongly sum-free subsets of abelian groups	1996	Tomasz Łuczak Tomasz Schoen

Common Coauthors

Coauthor	Papers Together
Ilya D. Shkredov	22
Tomasz Łuczak	12
Ernie Croot	3
Olof Sisask	3
Karol Cwalina	3
Andreas Baltz	2
Vsevolod F. Lev	2
Christian Reiher	2
Benjamin Doerr	2
Mirosława Jańczak	1
Anand Srivastav	1
Rafał Bystrzycki	1
Geir Agnarsson	1
Urban Larsson	1
Manuel Silva	1
Imre Z. Ruzsa	1
Oleg Pikhurko	1
Jonas Knape	1
Peter Hegarty	1
Noga Alon	1
Tomasz Kosciuszko	1
Vojtěch Rödl	1
Paulius Šarka	1
Artūras Dubickas	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	On Roth's theorem on progressions	2011	Tom Sanders	14
+	On Certain Sets of Integers	1953	K. F. Roth	13
+	A polynomial bound in Freiman's theorem	2002	Mei-Chu Chang	12
+	On Triples in Arithmetic Progression	1999	Jean Bourgain	12
+	Additive Combinatorics	2006	Terence Tao Van H. Vu	9
+ PDF Chat	On the Bogolyubov–Ruzsa lemma	2012	Tom Sanders	9
+ PDF Chat	Solving a linear equation in a set of integers I	1993	Imre Z. Ruzsa	8
+	Near optimal bounds in Freiman's theorem	2011	Tomasz Schoen	8
+	Roth’s theorem on progressions revisited	2008	Jean Bourgain	8
+	On Sets of Integers Which Contain No Three Terms in Arithmetical Progression	1946	Felix Behrend	7
+ PDF Chat	An improved construction of progression-free sets	2011	Michael Elkin	7
+	Structure in additively nonsmoothing sets	2011	Michael Bateman Nets Hawk Katz	6
+	Integer Sets Containing No Arithmetic Progressions	1987	D. R. Heath‐Brown	6
+	Sets with large additive energy and symmetric sets	2010	Ilya D. Shkredov Sergey Yekhanin	6
+ PDF Chat	Arithmetic progressions in sparse sumsets	2012	Ernie Croot Imre Z. Ruzsa Tomasz Schoen	6
+ PDF Chat	On Additive Doubling and Energy	2010	Nets Hawk Katz Paul Koester	6
+	A new proof of Szemerédi's theorem	2001	W. T. Gowers	6
+ PDF Chat	New bounds on cap sets	2011	Michael Bateman Nets Hawk Katz	6
+	Arithmetic progressions in sumsets	2002	B. Green	6
+ PDF Chat	Roth’s theorem in many variables	2013	Tomasz Schoen Ilya D. Shkredov	5
+	Extremal problems in discrete geometry	1983	Endre Szemerédi W. T. Trotter	5
+	Generalized arithmetical progressions and sumsets	1994	Imre Z. Ruzsa	5
+	A Note on Elkin’s Improvement of Behrend’s Construction	2010	Ben Green Julia Wolf	5
+ PDF Chat	A Probabilistic Technique for Finding Almost-Periods of Convolutions	2010	Ernie Croot Olof Sisask	5
+ PDF Chat	Additive structures in sumsets	2008	Tom Sanders	5
+ PDF Chat	On certain other sets of integers	2012	Tom Sanders	5
+	A statistical theorem of set addition	1994	Antal Balog Endre Szemer�di	5
+	Integer sets containing no arithmetic progressions	1990	Endre Szemerédi	4
+ PDF Chat	On sets of large exponential sums	2006	Ilya D. Shkredov	4
+ PDF Chat	Unsolved Problems in Number Theory	1994	Richard K. Guy	4
+ PDF Chat	Freiman's theorem in an arbitrary abelian group	2007	Ben Green Imre Z. Ruzsa	4
+ PDF Chat	ON A NONABELIAN BALOG–SZEMERÉDI-TYPE LEMMA	2010	Tom Sanders	4
+	On a theorem of Shkredov	2008	Tom Sanders	4
+	Combinatorial Number Theory and Additive Group Theory	2009	Alfred Geroldinger Imre Z. Ruzsa	4
+	ADDITIVE PROPERTIES OF MULTIPLICATIVE SUBGROUPS OF Fp	2011	Tomasz Schoen Ilya D. Shkredov	4
+ PDF Chat	Structure in Sets with Logarithmic Doubling	2011	Tom Sanders	4
+ PDF Chat	A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1.	2016	Thomas F. Bloom	4
+ PDF Chat	ROTH’S THEOREM FOR FOUR VARIABLES AND ADDITIVE STRUCTURES IN SUMS OF SPARSE SETS	2016	Tomasz Schoen Olof Sisask	4
+	On sumsets of dissociated sets	2007	Ilya D. Shkredov	4
+ PDF Chat	On a problem of Konyagin	2008	Tomasz Łuczak Tomasz Schoen	4
+	On Infinite Sum-free Sets of Natural Numbers	1997	Tomasz Łuczak Tomasz Schoen	4
+ PDF Chat	On sets of integers containing k elements in arithmetic progression	1975	Endre Szemerédi	4
+	Independent sets in regular graphs and sum-free subsets of finite groups	1991	Noga Alon	4
+	Character sums with exponential functions	2000	John Friedlander Jan Hansen Igor E. Shparlinski	3
+	Tight bounds on additive Ramsey-type numbers	2017	Karol Cwalina Tomasz Schoen	3
+	Absch�tzung der asymptotischen Dichte von Summenmengen	1953	Martin Kneser	3
+ PDF Chat	ADDITIVE DIMENSION AND A THEOREM OF SANDERS	2015	Tomasz Schoen Ilya D. Shkredov	3
+ PDF Chat	On an Additive Representation Associated with the $L_1$-Norm of an Exponential Sum	2007	M. Z. Garaev	3
+	Sum-Free Sets and Related Sets	1998	Yuri Bilu	3
+	Ein Satz �ber abelsche Gruppen mit Anwendungen auf die Geometrie der Zahlen	1954	Martin Kneser	3