Ernie Croot

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All published works

Action	Title	Year	Authors
+ PDF Chat	An inverse theorem for generalized arithmetic progression with mild multiplicative property	2024	Ernie Croot Junjie Mao
+ PDF Chat	Past and future of the cap set problem	2024	Ernie Croot Vsevolod F. Lev Péter Pál Pach
+ PDF Chat	On a conjecture of Graham on the p$p$‐divisibility of central binomial coefficients	2024	Ernie Croot Hamed Mousavi Maxie Schmidt
+ PDF Chat	Sums of the Form 1/x1^k + ... + 1/xn^k Modulo a Prime	2023	Ernie Croot
+	Prime sum graphs and the induced trees they contain	2023	Ernie Croot Patrick Jin
+	On the image of convolutions along an arithmetic progression	2023	Ernie Croot Chi-Nuo Lee
+	On a conjecture of Graham on the p-divisibility of central binomial coefficients	2022	Ernie Croot Hamed Mousavi Maxie Schmidt
+	On a Class of Sums with Unexpectedly High Cancellation, and its Applications	2019	Ernie Croot Hamed Mousavi
+	On a Class of Sums with Unexpectedly High Cancellation, and its Applications	2019	Ernie Croot Hamed Mousavi
+ PDF Chat	Few products, many h-fold sums	2018	Albert Bush Ernie Croot
+ PDF Chat	Progression-free sets in $\mathbb{Z}_4^n$ are exponentially small	2016	Ernie Croot Vsevolod F. Lev Péter Pál Pach
+	New Applications of the Polynomial Method to Problems in Combinatorics	2016	Ernie Croot
+	Progression-free sets in Z_4^n are exponentially small	2016	Ernie Croot Vsevolod F. Lev Péter Pál Pach
+	Progression-free sets in Z_4^n are exponentially small	2016	Ernie Croot Vsevolod F. Lev Péter Pál Pach
+ PDF Chat	A purely combinatorial approach to simultaneous polynomial recurrence modulo 1	2015	Ernie Croot Neil Lyall Alex Rice
+	Order-preserving Freiman isomorphisms	2014	Gagik Amirkhanyan Albert Bush Ernie Croot
+	Order-preserving Freiman isomorphisms	2014	Gagik Amirkhanyan Albert Bush Ernie Croot
+	Few products, many h-fold sums	2014	Albert Bush Ernie Croot
+ PDF Chat	Polynomials and Primes in Generalized Arithmetic Progressions	2014	Ernie Croot Neil Lyall Alex Rice
+	Order-preserving Freiman isomorphisms	2014	Gagik Amirkhanyan Albert Bush Ernie Croot
+	Few products, many h-fold sums	2014	Albert Bush Ernie Croot
+	Polynomials and Primes in Generalized Arithmetic Progressions	2013	Ernie Croot Neil Lyall Alex Rice
+	A Purely Combinatorial Approach to Simultaneous Polynomial Recurrence Modulo 1	2013	Ernie Croot Neil Lyall Alex Rice
+ PDF Chat	Arithmetic Progressions in Sumsets and <i>L<sup>p</sup></i>-Almost-Periodicity	2013	Ernie Croot Izabella Łaba Olof Sisask
+	Polynomials and Primes in Generalized Arithmetic Progressions (Revised Version)	2013	Ernie Croot Neil Lyall Alex Rice
+	Sets of Rich Lines in General Position	2013	Gagik Amirkhanyan Albert Bush Ernie Croot Chris Pryby
+	A Purely Combinatorial Approach to Simultaneous Polynomial Recurrence Modulo 1	2013	Ernie Croot Neil Lyall Alex Rice
+ PDF Chat	Some Properties of Lower Level-Sets of Convolutions	2012	Ernie Croot
+ PDF Chat	On sharp transitions in making squares	2012	Ernie Croot Andrew Granville Robin Pemantle Prasad Tetali
+ PDF Chat	Arithmetic progressions in sparse sumsets	2012	Ernie Croot Imre Z. Ruzsa Tomasz Schoen
+	Some properties of lower level-sets of convolutions	2011	Ernie Croot
+	Arithmetic progressions in sumsets and L^p-almost-periodicity	2011	Ernie Croot Izabella Łaba Olof Sisask
+ PDF Chat	On a Certain Generalization of the Balog–Szemerédi–Gowers Theorem	2011	Evan Borenstein Ernie Croot
+ PDF Chat	Sum-Product Inequalities with Perturbation	2011	Spencer Backman Ernie Croot Mariah Hamel Derrick Hart
+	Some properties of lower level-sets of convolutions	2011	Ernie Croot
+	Arithmetic progressions in sumsets and L^p-almost-periodicity	2011	Ernie Croot Izabella Łaba Olof Sisask
+ PDF Chat	A Probabilistic Technique for Finding Almost-Periods of Convolutions	2010	Ernie Croot Olof Sisask
+ PDF Chat	On the Structure of Sets with Few Three-Term Arithmetic Progressions	2010	Ernie Croot
+	A probabilistic technique for finding almost-periods of convolutions	2010	Ernie Croot Olof Sisask
+ PDF Chat	On Rich Lines in Grids	2010	Evan Borenstein Ernie Croot
+	On sums and products in ℂ[x]	2010	Ernie Croot Derrick Hart
+ PDF Chat	<i>h</i>-Fold Sums from a Set with Few Products	2010	Ernie Croot Derrick Hart
+	A probabilistic technique for finding almost-periods of convolutions	2010	Ernie Croot Olof Sisask
+	Sum-product inequalities with perturbation	2009	Spencer Backman Ernie Croot Derrick Hart Mariah Hamel
+	k-fold sums from a set with few products	2009	Ernie Croot Derrick Hart
+ PDF Chat	On sumsets and spectral gaps	2008	Ernie Croot Tomasz Schoen
+	On sums and products in C[x]	2008	Ernie Croot Derrick Hart
+ PDF Chat	A new proof of Roth’s theorem on arithmetic progressions	2008	Ernie Croot Olof Sisask
+	On rich lines in grids	2008	Evan Borenstein Ernie Croot
+ PDF Chat	The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit	2008	Ernie Croot
+	Sharp Transitions in Making Squares	2008	Ernie Croot Andrew Granville Robin Pemantle Prasad Tetali
+	A new proof of Roth's theorem on arithmetic progressions	2008	Ernie Croot Olof Sisask
+	On a certain generalization of the Balog-Szemeredi-Gowers Theorem	2008	Ernie Croot Evan Borenstein
+	On rich lines in grids	2008	Evan Borenstein Ernie Croot
+	On the decay of the Fourier transform and three term arithmetic progressions	2007	Ernie Croot
+	On equitable zero sums	2007	Ernie Croot Christian Elsholtz
+ PDF Chat	SMOOTH NUMBERS IN SHORT INTERVALS	2007	Ernie Croot
+	On a combinatorial method for counting smooth numbers in sets of integers	2007	Ernie Croot
+	An application of linear programming duality to discrete Fourier analysis and additive problems	2007	Ernie Croot
+	Arithmetic structures in smooth subsets of F_p	2007	Ernie Croot
+	The structure of critical sets for F_p arithmetic progressions	2007	Ernie Croot
+	On Sumsets and Spectral Gaps	2007	Ernie Croot Tomasz Schoen
+	On equitable zero sums	2007	Ernie Croot Christian Elsholtz
+	Subsets of F_p^n without three term arithmetic progressions have several large Fourier coefficients	2007	Ernie Croot
+	Complexity of inverting the Euler function	2006	Scott Contini Ernie Croot Igor E. Shparlinski
+	On the Decay of the Fourier Transform and Three Term Arithmetic Progressions	2006	Ernie Croot
+	On the Structure of Sets with Few Three-Term Arithmetic Progressions	2006	Ernie Croot
+	Long arithmetic progressions in critical sets	2005	Ernie Croot
+	The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit	2005	Ernie Croot
+	Complexity of Inverting the Euler Function	2004	Scott Contini Ernie Croot Igor E. Shparlinski
+	Complexity of Inverting the Euler Function	2004	Scott Contini Ernie Croot Igor E. Shparlinski
+	k-term Arithmetic Progressions in Sumsets	2004	Ernie Croot
+	Sums of the Form 1/x_1^k + ... + 1/x_n^k Modulo a Prime	2004	Ernie Croot
+	Long Arithmetic Progressions in Critical Sets	2004	Ernie Croot
+	A Structure Theorem for Positive Density Sets Having the Minimal Number of 3-term Arithmetic Progressions	2003	Ernie Croot
+	Memory Efficient Arithmetic	2003	Ernie Croot
+	A Combinatorial Method for Counting Smooth Numbers in Sets of Integers	2003	Ernie Croot
+	On Thin Sets of Primes Expressible as Sumsets	2002	Ernie Croot Christian Elsholtz
+	On Non-intersecting Arithmetic Progressions	2002	Ernie Croot
+	On the Oscillations of Multiplicative Functions Taking Values +/- 1	2002	Ernie Croot

Common Coauthors

Coauthor	Papers Together
Olof Sisask	8
Albert Bush	7
Alex Rice	6
Derrick Hart	6
Neil Lyall	6
Evan Borenstein	5
Vsevolod F. Lev	4
Péter Pál Pach	4
Gagik Amirkhanyan	4
Hamed Mousavi	4
Igor E. Shparlinski	3
Tomasz Schoen	3
Izabella Łaba	3
Scott Contini	3
Christian Elsholtz	3
Prasad Tetali	2
Andrew Granville	2
Maxie Schmidt	2
Spencer Backman	2
Robin Pemantle	2
Mariah Hamel	2
Chris Pryby	1
Chi-Nuo Lee	1
Junjie Mao	1
Patrick Jin	1
Imre Z. Ruzsa	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On Certain Sets of Positive Density	1959	P. Varnavides	12
+	Arithmetic progressions in sumsets	2002	B. Green	11
+ PDF Chat	On the number of sums and products	1997	György Elekes	10
+	On Certain Sets of Integers	1953	K. F. Roth	9
+ PDF Chat	On sums and products of integers	1997	Melvyn B. Nathanson	8
+ PDF Chat	Arithmetic progressions in sumsets	1991	Imre Z. Ruzsa	8
+ PDF Chat	On sums and products of integers	1983	Péter L. Erdős Endre Szemerédi	7
+	An Application of Graph Theory to Additive Number Theory	1985	Noga Alon P. Erdős	7
+ PDF Chat	On the Bogolyubov–Ruzsa lemma	2012	Tom Sanders	7
+	On Triples in Arithmetic Progression	1999	Jean Bourgain	6
+ PDF Chat	Arithmetic progressions in sparse sumsets	2012	Ernie Croot Imre Z. Ruzsa Tomasz Schoen	5
+	Extremal problems in discrete geometry	1983	Endre Szemerédi W. T. Trotter	5
+	A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four	1998	W. T. Gowers	5
+ PDF Chat	Shifted primes without large prime factors	1998	Roger C. Baker G. Harman	5
+	On subsets of finite abelian groups with no 3-term arithmetic progressions	1995	Roy Meshulam	5
+	Integer Sets Containing No Arithmetic Progressions	1987	D. R. Heath‐Brown	5
+	On arithmetic progressions in sums of sets of integers	2012	Jean Bourgain	5
+	Sums and Products from a Finite Set of Real Numbers	1998	Kevin Ford	5
+	Additive Combinatorics	2006	Terence Tao Van H. Vu	5
+	Bounding multiplicative energy by the sumset	2009	József Solymosi	5
+ PDF Chat	On sum-sets and product-sets of complex numbers	2005	József Solymosi	5
+	Prime Numbers: A Computational Perspective	2012	Richard E. Crandall Carl Pomerance	5
+ PDF Chat	On the size of $k$-fold sum and product sets of integers	2003	Jean Bourgain Mei-Chu Chang	5
+ PDF Chat	Additive structures in sumsets	2008	Tom Sanders	5
+	A polynomial bound in Freiman's theorem	2002	Mei-Chu Chang	4
+	None	1998	Kevin R. Ford	4
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum	4
+ PDF Chat	The Erdős–Szeméredi problem on sum set and product set	2003	Mei-Chu Chang	4
+	Optimal Representations by Sumsets and Subset Sums	1997	Vsevolod F. Lev	4
+ PDF Chat	On a problem of Konyagin	2008	Tomasz Łuczak Tomasz Schoen	4
+	Probability Inequalities for Sums of Independent Random Variables	1971	D. Kh. Fuk S. V. Nagaev	4
+	Finite addition theorems, I	1989	Andràs Sárközy	4
+	An old new proof of Roth’s theorem	2007	Endre Szemerédi	3
+	There are Infinitely Many Carmichael Numbers	1994	W. R. Alford Andrew Granville Carl Pomerance	3
+ PDF Chat	On Roth's theorem on progressions	2011	Tom Sanders	3
+ PDF Chat	The distribution of values of the Euler function	1972	Paul Bateman	3
+	Euler’s Function in Residue Classes	1998	Thomas P. Dence Carl Pomerance	3
+ PDF Chat	Multiplicative structure of values of the Euler function	2004	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski	3
+ PDF Chat	A sum-product estimate in finite fields, and applications	2004	Jean Bourgain Nets Hawk Katz Terence Tao	3
+ PDF Chat	Values of the Euler Function in Various Sequences	2005	William D. Banks Kevin Ford Florian Luca Francesco Pappalardi Igor E. Shparlinski	3
+	On subsets of abelian groups with no 3-term arithmetic progression	1987	Péter Frankl Ronald Graham V. Rödl	3
+	Popular values of Euler's function	1980	Carl Pomerance	3
+	Roth’s theorem on progressions revisited	2008	Jean Bourgain	3
+	Integer sets containing no arithmetic progressions	1990	Endre Szemerédi	3
+ PDF Chat	Residue classes free of values of Euler’s function	1999	Kevin Ford Sergeĭ Konyagin Carl Pomerance	3
+	The Prime k-Tuplets Conjecture on Average	1990	Antal Balog	3
+ PDF Chat	Factoring Integers with Elliptic Curves	1987	H. W. Lenstra	3
+	Integer Sum Sets Containing Long Arithmetic Progressions	1992	Gregory A. Freiman H. Halberstam Imre Z. Ruzsa	3
+ PDF Chat	PRIMES is in P	2004	Manindra Agrawal Neeraj Kayal Nitin Saxena	3
+	On the Decay of the Fourier Transform and Three Term Arithmetic Progressions	2006	Ernie Croot	2