H. A. Helfgott

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All published works

Action	Title	Year	Authors
+	New Dimensional Estimates for Subvarieties of Linear Algebraic Groups	2024	Jitendra Bajpai Daniele Dona H. A. Helfgott
+	New dimensional estimates for subvarieties of linear algebraic groups	2023	Jitendra Bajpai Daniele Dona H. A. Helfgott
+ PDF	Summing $$\mu (n)$$: a faster elementary algorithm	2022	H. A. Helfgott Lola Thompson
+ PDF	Explicit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup></mml:math> bounds for the Riemann <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ζ</mml:mi></mml:math> function	2022	Daniele Dona H. A. Helfgott Sebastian Zuniga Alterman
+ PDF	Optimality for the two-parameter quadratic sieve	2022	Emanuel Carneiro Andrés Chirre H. A. Helfgott Julián Mejía-Cordero
+	Aritmética, Grupos y Análisis (AGRA II, Cusco, Perú)	2022	Mikhail Belolipetsky H. A. Helfgott Carlos Gustavo Moreira
+	Expansion, divisibility and parity: an explanation	2022	H. A. Helfgott
+ PDF Chat	Expansion, Divisibility and Parity: An Explanation	2022	H. A. Helfgott
+	Growth estimates and diameter bounds for classical Chevalley groups	2021	Jitendra Bajpai Daniele Dona H. A. Helfgott
+	Summing $\mu(n)$: a faster elementary algorithm	2021	H. A. Helfgott Lola Thompson
+	Expansion, divisibility and parity	2021	H. A. Helfgott Maksym Radziwiłł
+	Growth estimates and diameter bounds for classical Chevalley groups	2021	Jitendra Bajpai Daniele Dona H. A. Helfgott
+	Summing $μ(n)$: a faster elementary algorithm	2021	H. A. Helfgott Lola Thompson
+	Optimality for the two-parameter quadratic sieve	2020	Emanuel Carneiro Andrés Chirre H. A. Helfgott Julián Mejía-Cordero
+	Explicit $L^2$ bounds for the Riemann $\zeta$ function	2019	Daniele Dona H. A. Helfgott Sebastian Zuniga Alterman
+ PDF Chat	Growth in Linear Algebraic Groups and Permutation Groups: Towards a Unified Perspective	2019	H. A. Helfgott
+	An improved sieve of Eratosthenes	2019	H. A. Helfgott
+	Growth and expansion in algebraic groups over finite fields	2019	H. A. Helfgott
+ PDF Chat	Growth and expansion in algebraic groups over finite fields	2019	H. A. Helfgott
+	Isomorphismes de graphes en temps quasi-polynomial (d’après Babai et Luks, Weisfeiler-Leman, ...)	2019	H. A. Helfgott
+	Explicit $L^2$ bounds for the Riemann $ζ$ function	2019	Daniele Dona H. A. Helfgott Sebastian Zuniga Alterman
+	Growth and expansion in algebraic groups over finite fields	2019	H. A. Helfgott
+	Primos, paridad y an\'alisis	2018	H. A. Helfgott Adrián Ubis
+	Soficity, short cycles, and the Higman group	2018	H. A. Helfgott Kate Juschenko
+	Machine-Assisted Proofs (ICM 2018 Panel)	2018	James H. Davenport Bjorn Poonen James Maynard H. A. Helfgott Pham Huu Tiep Luís Cruz-Filipe
+	Crecimiento y expansion en SL_2	2018	H. A. Helfgott
+	Growth in linear algebraic groups and permutation groups: towards a unified perspective	2018	H. A. Helfgott
+	Primos, paridad y análisis	2018	H. A. Helfgott Adrián Ubis
+	An improved sieve of Eratosthenes	2017	H. A. Helfgott
+	Isomorphismes de graphes en temps quasi-polynomial (d'après Babai et Luks, Weisfeiler-Leman...)	2017	H. A. Helfgott
+	Graph isomorphisms in quasi-polynomial time	2017	H. A. Helfgott Jitendra Bajpai Daniele Dona
+	An improved sieve of Eratosthenes	2017	H. A. Helfgott
+	Soficity, short cycles and the Higman group	2015	H. A. Helfgott Kate Juschenko
+ PDF	On growth in an abstract plane	2015	Nick Gill H. A. Helfgott Misha Rudnev
+ PDF	Growth in groups: ideas and perspectives	2015	H. A. Helfgott
+ PDF	On the dimension of additive sets	2015	Pablo Candela H. A. Helfgott
+	Soficity, short cycles and the Higman group	2015	H. A. Helfgott Kate Juschenko
+	The ternary Goldbach problem	2015	H. A. Helfgott
+	Random generators of the symmetric group: Diameter, mixing time and spectral gap	2014	H. A. Helfgott Ákos Seress Andrzej Żuk
+	The ternary Goldbach problem	2014	H. A. Helfgott
+ PDF	Growth in solvable subgroups of $${{\mathrm{GL}}}_r({\mathbb {Z}}/p{\mathbb {Z}})$$ GL r ( Z / p Z )	2014	Nick Gill H. A. Helfgott
+	MAXIMA AND MINIMA BEFORE CALCULUS	2014	H. A. Helfgott Michel Helfgott
+ PDF	On the diameter of permutation groups	2014	H. A. Helfgott Ákos Seress
+	On the dimension of additive sets	2014	Pablo Candela H. A. Helfgott
+ PDF	Square-free values of f(p), f cubic	2014	H. A. Helfgott
+	La conjecture de Golbach ternaire	2014	H. A. Helfgott
+	The ternary Goldbach problem	2014	H. A. Helfgott
+	Random generators of the symmetric group: diameter, mixing time and spectral gap	2013	H. A. Helfgott Ákos Seress Andrzej Żuk
+	Numerical Verification of the Ternary Goldbach Conjecture up to 8.875·10<sup>30</sup>	2013	H. A. Helfgott David J. Platt
+ PDF	Bounds on the diameter of Cayley graphs of the symmetric group	2013	John Bamberg Nick Gill Thomas P. Hayes H. A. Helfgott Ákos Seress Pablo Spiga
+	Major arcs for Goldbach's theorem	2013	H. A. Helfgott
+	Major arcs for Goldbach's theorem	2013	H. A. Helfgott
+	The ternary Goldbach conjecture is true	2013	H. A. Helfgott
+	Growth in groups: ideas and perspectives	2013	H. A. Helfgott
+	Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30	2013	H. A. Helfgott David J. Platt
+	Random generators of the symmetric group: diameter, mixing time and spectral gap	2013	H. A. Helfgott Ákos Seress Andrzej Żuk
+	On growth in an abstract plane	2012	Nick Gill H. A. Helfgott Misha Rudnev
+	Bounds on the diameter of Cayley graphs of the symmetric group	2012	John Bamberg Nick Gill Thomas P. Hayes H. A. Helfgott Ákos Seress Pablo Spiga
+	Minor arcs for Goldbach's problem	2012	H. A. Helfgott
+	Bounds on the diameter of Cayley graphs of the symmetric group	2012	John Bamberg Nick Gill Thomas Hayes H. A. Helfgott Ákos Seress Pablo Spiga
+	On the diameter of permutation groups	2011	H. A. Helfgott Ákos Seress
+	Deterministic methods to find primes	2011	Terence Tao Ernest S. Croot H. A. Helfgott
+ PDF	Growth in $\mathrm{SL}_3(ℤ/pℤ)$	2011	H. A. Helfgott
+	Groupes, courbes et croissance	2011	H. A. Helfgott
+	Square-free values of f(p), f cubic	2011	H. A. Helfgott
+	On the diameter of permutation groups	2011	H. A. Helfgott Ákos Seress
+ PDF	AN EXPLICIT INCIDENCE THEOREM IN	2010	H. A. Helfgott Misha Rudnev
+ PDF Chat	Growth of Small Generating Sets in SLn(Z/pZ)	2010	Nick Gill H. A. Helfgott
+	Growth in solvable subgroups of $GL_r(\mathbb{Z}/p\mathbb{Z})$	2010	Nick Gill H. A. Helfgott
+ PDF	Improving Roth's Theorem in the Primes	2010	H. A. Helfgott Anne de Roton
+	Growth of small generating sets in SL_n(Z/pZ)	2010	Nick Gill H. A. Helfgott
+	Growth in solvable subgroups of GL_r(Z/pZ)	2010	Nick Gill H. A. Helfgott
+	Growth of small generating sets in SL_n(Z/pZ)	2010	Nick Gill H. A. Helfgott
+	Azar y Aritmetica	2009	H. A. Helfgott
+	A Modern Vision of the Work of Cardano and Ferrari on Quartics	2009	H. A. Helfgott Michel Helfgott
+	Improving Roth's theorem in the primes	2009	H. A. Helfgott Anne de Roton
+	Azar y Aritmetica	2009	H. A. Helfgott
+ PDF Chat	Power-free values, repulsion between points, differing beliefs and the existence of error	2008	H. A. Helfgott
+	Growth in SL_3(Z/pZ)	2008	H. A. Helfgott
+ PDF	Growth and generation in SL<sub>2</sub>(ℤ∕pℤ)	2008	H. A. Helfgott
+	Growth in SL_3(Z/pZ)	2008	H. A. Helfgott
+ PDF	Power-free values, large deviations, and integer points on irrational curves	2007	H. A. Helfgott
+	Power-free values, repulsion between points, differing beliefs and the existence of error	2007	H. A. Helfgott
+ PDF Chat	THE PARITY PROBLEM FOR REDUCIBLE CUBIC FORMS	2006	H. A. Helfgott
+	Integral points on elliptic curves and 3-torsion in class groups	2006	H. A. Helfgott Akshay Venkatesh
+	Root numbers and ranks in positive characteristic	2005	Brian Conrad Keith Conrad H. A. Helfgott
+	Growth and generation in SL_2(Z/pZ)	2005	H. A. Helfgott
+	The parity problem for irreducible cubic forms	2005	H. A. Helfgott
+	Power-free values of polynomials and integer points on irrational curves	2004	H. A. Helfgott
+	On the behaviour of root numbers in families of elliptic curves	2004	H. A. Helfgott
+	The parity problem for reducible cubic forms	2004	H. A. Helfgott
+	Integral points on elliptic curves and 3-torsion in class groups	2004	H. A. Helfgott Akshay Venkatesh
+	Root numbers and ranks in positive characteristic	2004	Brian Conrad Keith Conrad H. A. Helfgott
+	Power-free values, large deviations, and integer points on irrational curves	2004	H. A. Helfgott
+ PDF	On the square-free sieve	2004	H. A. Helfgott
+	Root numbers and the parity problem	2003	H. A. Helfgott
+	A noncalculus proof that Fermat’s principle of least time implies the law of refraction	2002	H. A. Helfgott Michel Helfgott
+	Edge Effects on Local Statistics in Lattice Dimers: A Study of the Aztec Diamond (Finite Case)	2000	H. A. Helfgott
+ PDF	Tilings of Diamonds and Hexagons with Defects	1999	H. A. Helfgott Ira M. Gessel
+	ENUMERATION OF TILINGS OF DIAMONDS AND HEXAGONS WITH DEFECTS	1999	H. A. Helfgott Ira M. Gessel
+	Enumeration of tilings of diamonds and hexagons with defects	1998	H. A. Helfgott Ira M. Gessel

Common Coauthors

Coauthor	Papers Together
Nick Gill	11
Ákos Seress	9
Daniele Dona	8
Jitendra Bajpai	5
Kate Juschenko	3
Michel Helfgott	3
Misha Rudnev	3
Lola Thompson	3
Andrzej Żuk	3
Pablo Spiga	3
John Bamberg	3
Ira M. Gessel	3
Sebastian Zuniga Alterman	3
Akshay Venkatesh	2
Julián Mejía-Cordero	2
Keith Conrad	2
Thomas P. Hayes	2
Adrián Ubis	2
Emanuel Carneiro	2
Pablo Candela	2
Andrés Chirre	2
David J. Platt	2
Brian Conrad	2
Anne de Roton	2
Ernest S. Croot	1
James Maynard	1
James H. Davenport	1
Mikhail Belolipetsky	1
Luís Cruz-Filipe	1
Bjorn Poonen	1
Pham Huu Tiep	1
Thomas Hayes	1
Carlos Gustavo Moreira	1
Maksym Radziwiłł	1
Terence Tao	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	Growth and generation in SL<sub>2</sub>(ℤ∕pℤ)	2008	H. A. Helfgott	15
+	On the diameter of permutation groups	1992	László Babai Ákos Seress	15
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	14
+ PDF Chat	Approximate Subgroups of Linear Groups	2011	Emmanuel Breuillard Ben Green Terence Tao	14
+ PDF	Uniform expansion bounds for Cayley graphs of SL<sub>2</sub>(𝔽<sub>p</sub>)	2008	Jean Bourgain Alex Gamburd	13
+ PDF Chat	On uniform exponential growth for linear groups	2005	Alex Eskin Shahar Mozes Hee Oh	11
+ PDF	Growth in $\mathrm{SL}_3(ℤ/pℤ)$	2011	H. A. Helfgott	11
+ PDF Chat	Product set estimates for non-commutative groups	2008	Terence Tao	10
+ PDF Chat	A sum-product estimate in finite fields, and applications	2004	Jean Bourgain Nets Hawk Katz Terence Tao	10
+ PDF	On the square-free sieve	2004	H. A. Helfgott	10
+	Finite subgroups of algebraic groups	2011	Michael Larsen Richard Pink	9
+	On the diameter of the symmetric group: polynomial bounds	2004	László Babai Robert Beals Ákos Seress	9
+ PDF	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak	9
+	Stable group theory and approximate subgroups	2011	Ehud Hrushovski	9
+	On the spectral gap for finitely-generated subgroups of SU(2)	2007	Jean Bourgain Alex Gamburd	9
+	POWER-FREE VALUES OF BINARY FORMS	1992	George Greaves	8
+	Near-independence of permutations and an almost sure polynomial bound on the diameter of the symmetric group	2005	László Babai Thomas P. Hayes	8
+ PDF	Product decompositions of quasirandom groups and a Jordan type theorem	2011	Nikolay Nikolov László Pyber	8
+	Multiplicative Number Theory	1980	H. Davenport	8
+	Growth in SL2 over finite fields	2010	Oren Dinai	8
+	Extremal problems in discrete geometry	1983	Endre Szemerédi W. T. Trotter	8
+	Applications of sieve methods to the theory of numbers	1976	C. Hooley	8
+	Bounds for multiplicities of automorphic representations	1991	Peter Sarnak Xiaoxi Xue	8
+	On the orders of doubly transitive permutation groups, elementary estimates	1993	L. Pyber	8
+	On the order of doubly transitive permutation groups	1982	László Babai	8
+	Growth in finite simple groups of Lie type of bounded rank	2010	László Pyber Endre Szabó	7
+ PDF	Approximate multiplicative groups in nilpotent Lie groups	2010	David Fisher Nets Hawk Katz Irine Peng	7
+	None	1998	Andrew Granville	7
+ PDF	On the diameter of permutation groups	2014	H. A. Helfgott Ákos Seress	7
+ PDF Chat	Additive properties of product sets in fields of prime order	2007	A. Glibichuk Sergeĭ Konyagin	7
+	The Riemann Hypothesis and Hilbert's Tenth Problem.	1966	L. Carlitz S. Chowla	7
+	On the diameter of cayley graphs of the symmetric group	1988	László Babai Ákos Seress	7
+	On the diameter of Eulerian orientations of graphs	2006	László Babai	7
+ PDF	On the number of sums and products	1997	György Elekes	7
+ PDF	On sums and products of integers	1983	Péter L. Erdős Endre Szemerédi	6
+ PDF Chat	Expansion in perfect groups	2012	Alireza Salehi Golsefidy Péter P. Varjú	6
+ PDF	The Arithmetic of Elliptic Curves	1986	Joseph H. Silverman	6
+	Graphs with automorphism groups admitting composition factors of bounded rank	2011	Cheryl E. Praeger László Pyber Pablo Spiga Endre Szabó	6
+ PDF Chat	The structure of approximate groups	2012	Emmanuel Breuillard Ben Green Terence Tao	6
+	Growth in finite simple groups of Lie type	2014	László Pyber Endre Szabó	6
+	Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸	2013	Tomás Oliveira e Silva Siegfried Herzog Silvio Pardi	6
+ PDF	Comparison Techniques for Random Walk on Finite Groups	1993	Persi Diaconis Laurent Saloff‐Coste	6
+	Root numbers and the parity problem	2003	H. A. Helfgott	6
+	A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.	1987	Joseph H. Silverman	6
+	The number of integral points on arcs and ovals	1989	Enrico Bombieri Jonathan Pila	6
+	On the behaviour of root numbers in families of elliptic curves	2004	H. A. Helfgott	6
+	Arithmetical Properties of Polynomials	1953	P. Erdős	6
+	The rank of elliptic curves	1977	Armand Brumer Kenneth Kramer	6
+	Growth in solvable subgroups of GL_r(Z/pZ)	2010	Nick Gill H. A. Helfgott	6
+	Quasirandom Groups	2008	W. T. Gowers	6