Xuancheng Shao

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All published works

Action	Title	Year	Authors
+	Density versions of the binary Goldbach problem	2025	Ali Alsetri Xuancheng Shao
+ PDF	Additive energies of subsets of discrete cubes	2024	Xuancheng Shao
+ PDF Chat	Sums of Kloosterman sums over square-free and smooth integers	2024	Xuancheng Shao Igor E. Shparlinski Laurence P. Wijaya
+ PDF Chat	Higher uniformity of arithmetic functions in short intervals II. Almost all intervals	2024	Kaisa Matomäki Maksym Radziwiłł Xuancheng Shao Terence Tao Joni Teräväinen
+ PDF	Bounds in a popular multidimensional nonlinear Roth theorem	2024	Sarah Peluse Sean Prendiville Xuancheng Shao
+ PDF Chat	Bounds in a popular multidimensional nonlinear Roth theorem	2024	Sarah Peluse Sean Prendiville Xuancheng Shao
+ PDF Chat	Additive energies of subsets of discrete cubes	2024	Xuancheng Shao
+ PDF Chat	Density versions of the binary Goldbach problem	2024	Ali Alsetri Xuancheng Shao
+ PDF	A transference principle for systems of linear equations, and applications to almost twin primes	2023	Pierre‐Yves Bienvenu Xuancheng Shao Joni Teräväinen
+ PDF	A transference principle for systems of linear equations, and applications to almost twin primes	2023	Pierre‐Yves Bienvenu Xuancheng Shao Joni Teräväinen
+ PDF	Higher uniformity of arithmetic functions in short intervals I. All intervals	2023	Kaisa Matomäki Xuancheng Shao Terence Tao Joni Teräväinen
+ PDF Chat	Singmaster’s Conjecture In The Interior Of Pascal’s Triangle	2022	Kaisa Matomäki Maksym Radziwiłł Xuancheng Shao Terence Tao Joni Teräväinen
+	Higher uniformity of arithmetic functions in short intervals I. All intervals	2022	Kaisa Matomäki Xuancheng Shao Terence Tao Joni Teräväinen
+	On Hilbert cubes and primitive roots in finite fields	2021	Ali Alsetri Xuancheng Shao
+ PDF	The Bombieri-Vinogradov theorem for nilsequences	2021	Xuancheng Shao Joni Teräväinen
+	Singmaster's conjecture in the interior of Pascal's triangle	2021	Kaisa Matomäki Maksym Radziwiłł Xuancheng Shao Terence Tao Joni Teräväinen
+	Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of $\mathbb{F_p}$	2021	Ali Alsetri Xuancheng Shao
+	A transference principle for systems of linear equations, and applications to almost twin primes	2021	Pierre‐Yves Bienvenu Xuancheng Shao Joni Teräväinen
+	Singmaster's conjecture in the interior of Pascal's triangle	2021	Kaisa Matomäki Maksym Radziwiłł Xuancheng Shao Terence Tao Joni Teräväinen
+	The Bombieri-Vinogradov theorem for nilsequences	2020	Xuancheng Shao Joni Teräväinen
+ PDF	None	2019	Xuancheng Shao
+ PDF	Discorrelation Between Primes in Short Intervals and Polynomial Phases	2019	Kaisa Matomäki Xuancheng Shao
+	Bombieri-Vinogradov for multiplicative functions, and beyond the x1/2-barrier	2019	Andrew Granville Xuancheng Shao
+	Discorrelation between primes in short intervals and polynomial phases	2019	Kaisa Matomäki Xuancheng Shao
+	When the sieve works II	2018	Kaisa Matomäki Xuancheng Shao
+ PDF Chat	A robust version of Freiman's 3<i>k</i>–4 Theorem and applications	2018	Xuancheng Shao Wenqiang Xu
+ PDF Chat	Upper Tail Large Deviations for Arithmetic Progressions in a Random Set	2018	Bhaswar B. Bhattacharya Shirshendu Ganguly Xuancheng Shao Yufei Zhao
+	On an almost all version of the Balog-Szemeredi-Gowers theorem	2018	Xuancheng Shao
+ PDF	WHEN DOES THE BOMBIERI–VINOGRADOV THEOREM HOLD FOR A GIVEN MULTIPLICATIVE FUNCTION?	2018	Andrew Granville Xuancheng Shao
+ PDF Chat	Gowers norms of multiplicative functions in progressions on average	2017	Xuancheng Shao
+ PDF Chat	Vinogradov's theorem with almost equal summands	2017	Kaisa Matomäki James Maynard Xuancheng Shao
+ PDF Chat	Vinogradov’s three primes theorem with almost twin primes	2017	Kaisa Matomäki Xuancheng Shao
+	Bombieri-Vinogradov for multiplicative functions, and beyond the $x^{1/2}$-barrier	2017	Andrew Granville Xuancheng Shao
+	When does the Bombieri-Vinogradov Theorem hold for a given multiplicative function?	2017	Andrew Granville Xuancheng Shao
+ PDF	SMOOTH‐SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE ‐BARRIER	2017	Sary Drappeau Andrew Granville Xuancheng Shao
+ PDF Chat	Narrow Arithmetic Progressions in the Primes	2016	Xuancheng Shao
+ PDF Chat	On an inverse ternary Goldbach problem	2016	Xuancheng Shao
+ PDF	Weyl sums, mean value estimates, and Waring's problem with friable numbers	2016	Sary Drappeau Xuancheng Shao
+ PDF	Polynomial values modulo primes on average and sharpness of the larger sieve	2015	Xuancheng Shao
+	When the sieve works II	2015	Kaisa Matomäki Xuancheng Shao
+	Narrow arithmetic progressions in the primes	2015	Xuancheng Shao
+	Algebra & Number Theory	2015	Xuancheng Shao
+	When the sieve works II	2015	Kaisa Matomäki Xuancheng Shao
+ PDF	AN -FUNCTION-FREE PROOF OF VINOGRADOV’S THREE PRIMES THEOREM	2014	Xuancheng Shao
+ PDF Chat	A density version of the Vinogradov three primes theorem	2014	Xuancheng Shao
+ PDF Chat	Character sums over unions of intervals	2014	Xuancheng Shao
+ PDF Chat	Large values of the additive energy in and	2014	Xuancheng Shao
+	On an inverse ternary Goldbach problem	2014	Xuancheng Shao
+	Polynomial values modulo primes on average and sharpness of the larger sieve	2014	Xuancheng Shao
+	Carries, Group Theory, and Additive Combinatorics	2014	Persi Diaconis Xuancheng Shao K. Soundararajan
+ PDF Chat	On character sums and exponential sums over generalized arithmetic progressions	2013	Xuancheng Shao
+	Character sums over unions of intervals	2013	Xuancheng Shao
+	A New Proof of Vinogradov's Three Primes Theorem	2013	Xuancheng Shao
+	Carries, group theory, and additive combinatorics	2013	Persi Diaconis Xuancheng Shao K. Soundararajan
+	Finding linear patterns of complexity one	2013	Xuancheng Shao
+	Deformations of associahedra and visibility graphs	2012	Satyan L. Devadoss Rahul Shah Xuancheng Shao Ezra Winston
+	Visibility graphs and deformations of associahedra	2009	Satyan L. Devadoss Rahul Shah Xuancheng Shao Ezra Winston
+ PDF Chat	Generalizations of product-free subsets	2009	Kiran S. Kedlaya Xuancheng Shao
+ PDF Chat	Type-II/III DCT/DST algorithms with reduced number of arithmetic operations	2008	Xuancheng Shao Steven G. Johnson
+ PDF Chat	Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations	2008	Xuancheng Shao Steven G. Johnson
+	Generalizations of product-free subsets	2008	Kiran S. Kedlaya Xuancheng Shao

Common Coauthors

Coauthor	Papers Together
Kaisa Matomäki	13
Joni Teräväinen	11
Terence Tao	6
Andrew Granville	5
Maksym Radziwiłł	4
Pierre‐Yves Bienvenu	3
Satyan L. Devadoss	2
Ezra Winston	2
Persi Diaconis	2
Sarah Peluse	2
Sean Prendiville	2
K. Soundararajan	2
Kiran S. Kedlaya	2
Ali Alsetri	2
Sary Drappeau	2
Steven G. Johnson	2
Ali Alsetri	2
Yufei Zhao	1
James Maynard	1
Rahul Shah	1
Laurence P. Wijaya	1
Shirshendu Ganguly	1
Wenqiang Xu	1
Bhaswar B. Bhattacharya	1
Rahul Shah	1
Igor E. Shparlinski	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	The quantitative behaviour of polynomial orbits on nilmanifolds	2012	Ben Green Terence Tao	12
+ PDF	Linear equations in primes	2010	Ben Green Terence Tao	12
+ PDF	The primes contain arbitrarily long arithmetic progressions	2008	Benjamin Green Terence Tao	11
+	Analytic Number Theory	2004	Emmanuel Kowalski Henryk Iwaniec	10
+	Opera de Cribro	2010	John Friedlander Henryk Iwaniec	10
+ PDF	An inverse theorem for the Gowers U^(s+1)[N]-norm	2012	Ben Green Terence Tao Tamar Ziegler	8
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	7
+ PDF	The Möbius function is strongly orthogonal to nilsequences	2012	Ben Green Terence Tao	6
+ PDF	Bounded gaps between primes	2014	Zhang Yitang	6
+ PDF	AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM	2008	Ben Green Terence Tao	6
+ PDF Chat	Sum-free sets in abelian groups	2005	Ben Green Imre Z. Ruzsa	6
+	Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers	2012	Adam J. Harper	6
+ PDF	The Ternary Goldbach Problem	1985	D. R. Heath‐Brown	6
+	Higher order Fourier analysis of multiplicative functions and applications	2016	Nikos Frantzikinakis Bernard Host	5
+ PDF Chat	Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges	2018	Kaisa Matomäki Maksym Radziwiłł Terence Tao	5
+ PDF	Roth’s theorem in the primes	2005	Ben Green	5
+	Multiplicative Number Theory I: Classical Theory	2006	Hugh L. Montgomery R. C. Vaughan	5
+	Additive Combinatorics	2006	Terence Tao Van H. Vu	5
+ PDF	Primes in arithmetic progressions to large moduli	1986	Enrico Bombieri John Friedlander Henryk Iwaniec	5
+ PDF	Restriction theory of the Selberg sieve, with applications	2006	Ben Green Terence Tao	5
+ PDF	Multiplicative functions in short intervals	2016	Kaisa Matomäki Maksym Radziwiłł	5
+	On the representation of large odd integer as a sum of three almost equal primes	1991	Tao Zhan	5
+ PDF Chat	A density version of Vinogradov's three primes theorem	2010	Hongze Li Hao Pan	5
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum	4
+ PDF	Small gaps between primes	2014	James Maynard	4
+	Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers	2012	Adam J. Harper	4
+	A combinatorial proof of the Removal Lemma for Groups	2009	Daniel Kráľ Oriol Serra Lluís Vena	4
+ PDF	The Difference Between Consecutive Primes, II	2001	Roger C. Baker G. Harman J. Pintz	4
+	ON THE REPRESENTATION OF A LARGER EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES	1973	Chen Jing-Run	4
+ PDF	An inverse theorem for the Gowers $U^{s+1}[N]$-norm	2011	Tamar Ziegler Terence Tao Ben Green	4
+ PDF	SMOOTH‐SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE ‐BARRIER	2017	Sary Drappeau Andrew Granville Xuancheng Shao	4
+ PDF Chat	Vinogradov's theorem with almost equal summands	2017	Kaisa Matomäki James Maynard Xuancheng Shao	4
+ PDF Chat	The inverse sieve problem in high dimensions	2012	Miguel N. Walsh	4
+	On Character Sums and Primitive Roots<sup>†</sup>	1962	D. A. Burgess	4
+ PDF	Inverse questions for the large sieve	2014	Ben Green Adam J. Harper	4
+ PDF	Dense clusters of primes in subsets	2016	James Maynard	4
+	A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four	1998	W. T. Gowers	4
+	Generalized arithmetical progressions and sumsets	1994	Imre Z. Ruzsa	4
+	Entiers Sans Grand Facteur Premier En Progressions Arithmetiques	1991	Étienne Fouvry Gérald Tenenbaum	4
+	A Brun-Titschmarsh theorem for multiplicative functions.	1980	Peter Shiu	4
+ PDF Chat	A density version of the Vinogradov three primes theorem	2014	Xuancheng Shao	4
+ PDF	Uniformity norms, their weaker versions, and applications	2022	Pandelis Dodos Vassilis Kanellopoulos	4
+	Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis	1994	Hugh L. Montgomery	4
+ PDF	Integers without large prime factors	1993	Adolf Hildebrand Gérald Tenenbaum	4
+ PDF	The analytic principle of the large sieve	1978	Hugh L. Montgomery	4
+	Répartition Statistique Des Entiers Sans Grand Facteur Premier Dans Les Progressions Arithmétiques	1996	Étienne Fouvry Gérald Tenenbaum	4
+ PDF Chat	A relative Szemerédi theorem	2015	David Conlon Jacob Fox Yufei Zhao	4
+	On variants of the larger sieve	2004	Ernest S. Croot Christian Elsholtz	4
+	On addition of two distinct sets of integers	1995	Vsevolod F. Lev Pavel Y. Smeliansky	4
+ PDF Chat	Higher Order Fourier Analysis	2012	Terence Tao	4