Stanley Yao Xiao

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All published works

Action	Title	Year	Authors
+ PDF Chat	Hilbert's tenth problem for systems of diagonal quadratic forms, and B\"{u}chi's problem	2024	Stanley Yao Xiao
+	Prime values of f(a,b2) and f(a,p2), f quadratic	2024	Stanley Yao Xiao
+	Density of power-free values of polynomials II	2024	Kostadinka Lapkova Stanley Yao Xiao
+	Elliptic curves with a rational 2-torsion point ordered by conductor and the boundedness of average rank	2024	Stanley Yao Xiao
+ PDF Chat	Exponential sums over singular binary quartic forms and applications	2024	Yasuhiro Ishitsuka Takashi Taniguchi Frank Thorne Stanley Yao Xiao
+ PDF Chat	Heights and quantitative arithmetic on stacky curves	2024	Brett Nasserden Stanley Yao Xiao
+	Elliptic curves with a rational 2-torsion point ordered by conductor and the boundedness of average rank	2023	Stanley Yao Xiao
+	Quartic polynomials in two variables do not represent all non-negative integers	2023	Stanley Yao Xiao Shuntaro Yamagishi
+	Sextic polynomials in two variables do not represent all non-negative integers	2023	Stanley Yao Xiao
+	On monic abelian cubics	2022	Stanley Yao Xiao
+	Prime values of $f(a,b^2)$ and $f(a,p^2)$, $f$ quadratic	2021	Stanley Yao Xiao
+	Heights and quantitative arithmetic on stacky curves	2021	Brett Nasserden Stanley Yao Xiao
+	On the number of binary quadratic forms having discriminant $1-4p$, $p$ prime	2020	Alison Beth Miller Stanley Yao Xiao
+	The density of rational points on $\mathbb{P}^1$ with three stacky points	2020	Brett Nasserden Stanley Yao Xiao
+ PDF Chat	On the representation of $k$-free integers by binary forms	2020	Cameron L. Stewart Stanley Yao Xiao
+	The number of quartic 𝐷₄-fields with monogenic cubic resolvent ordered by conductor	2020	Cindy Tsang Stanley Yao Xiao
+ PDF Chat	On prime values of binary quadratic forms with a thin variable	2020	Peter Cho-Ho Lam Damaris Schindler Stanley Yao Xiao
+	A stratification result for an exponential sum modulo $p^2$	2020	Kostadinka Lapkova Stanley Yao Xiao
+	The density of rational points on $\mathbb{P}^1$ with three stacky points	2020	Brett Nasserden Stanley Yao Xiao
+	On the number of binary quadratic forms having discriminant $1-4p$, $p$ prime	2020	Alison Beth Miller Stanley Yao Xiao
+	Density of power-free values of polynomials II	2020	Kostadinka Lapkova Stanley Yao Xiao
+ PDF Chat	Binary quartic forms with bounded invariants and small Galois groups	2019	Cindy Tsang Stanley Yao Xiao
+	On the $\zeta_3$-Pell equation	2019	Erick Knight Stanley Yao Xiao
+	On monic abelian cubics	2019	Stanley Yao Xiao
+ PDF Chat	On the representation of integers by binary forms	2019	C. L. Stewart Stanley Yao Xiao
+ PDF Chat	Zeroes of Polynomials With Prime Inputs and Schmidt’s -invariant	2019	Stanley Yao Xiao Shuntaro Yamagishi
+ PDF Chat	On binary cubic and quartic forms	2019	Stanley Yao Xiao
+ PDF Chat	DENSITY OF POWER‐FREE VALUES OF POLYNOMIALS	2019	Kostadinka Lapkova Stanley Yao Xiao
+	The negative Pell equation	2019	Erick Knight Stanley Yao Xiao
+	Uniformity of fibres of period mappings and the $S$-unit equation	2019	Brett Nasserden Stanley Yao Xiao
+	On the $ζ_3$-Pell equation	2019	Erick Knight Stanley Yao Xiao
+	On monic abelian cubics	2019	Stanley Yao Xiao
+ PDF Chat	Square-free Values of Decomposable Forms	2017	Stanley Yao Xiao
+	On the representation of integers by binary quadratic forms	2017	Stanley Yao Xiao
+	Binary quartic forms with vanishing $J$-invariant	2017	Stanley Yao Xiao
+	On the representation of integers by binary quadratic forms	2017	Stanley Yao Xiao
+	Some results on binary forms and counting rational points on algebraic varieties	2016	Stanley Yao Xiao
+ PDF Chat	Power-Free Values of Binary Forms and the Global Determinant Method	2016	Stanley Yao Xiao
+	Zeroes of polynomials in many variables with prime inputs	2015	Stanley Yao Xiao Shuntaro Yamagishi
+	A Combinatorial Identity	2012	Kim McInturff Takis Konstantopoulos Stanley Yao Xiao
+	On the Erdös-Turán conjecture and related results	2011	Stanley Yao Xiao

Common Coauthors

Coauthor	Papers Together
Brett Nasserden	5
Kostadinka Lapkova	4
Erick Knight	3
Shuntaro Yamagishi	3
Alison Beth Miller	2
Cindy Tsang	2
C. L. Stewart	1
Damaris Schindler	1
Takis Konstantopoulos	1
Cameron L. Stewart	1
Kim McInturff	1
Peter Cho-Ho Lam	1
Takashi Taniguchi	1
Yasuhiro Ishitsuka	1
Frank Thorne	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	The Density of Rational Points on Curves and Surfaces	2002	D. R. Heath‐Brown	12
+ PDF Chat	Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves	2014	Manjul Bhargava Arul Shankar	11
+ PDF Chat	On the number of solutions of polynomial congruences and Thue equations	1991	C. L. Stewart	8
+ PDF Chat	On the power free values of polynomials	1967	C. Hooley	7
+ PDF Chat	On binary cubic and quartic forms	2019	Stanley Yao Xiao	7
+	On the power-free values of polynomials in two variables: II	2009	C. Hooley	7
+ PDF Chat	Reduction of Binary Cubic and Quartic Forms	1999	J. E. Cremona	6
+	POWER-FREE VALUES OF BINARY FORMS	1992	George Greaves	6
+	On the Number of Integers Which Can Be Represented By a Binary Form	1938	Paul Erdős K. Mahler	5
+ PDF Chat	Quantitative Arithmetic of Projective Varieties	2009	Timothy D. Browning	5
+	Arithmetical Properties of Polynomials	1953	P. Erdős	5
+ PDF Chat	Decomposable Form Inequalities	2001	Jeffrey Lin Thunder	5
+ PDF Chat	Power-Free Values of Binary Forms and the Global Determinant Method	2016	Stanley Yao Xiao	5
+ PDF Chat	On the representation of integers by binary forms	2019	C. L. Stewart Stanley Yao Xiao	4
+ PDF Chat	Square-free Values of Decomposable Forms	2017	Stanley Yao Xiao	4
+	None	1995	Trevor D. Wooley	4
+ PDF Chat	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld	4
+ PDF Chat	Counting rational points on algebraic varieties	2006	T. D. Browning D. R. Heath‐Brown Per Salberger	4
+	On Thue's equation	1987	Enrico Bombieri Wolfgang M. Schmidt	4
+ PDF Chat	On ranks of twists of elliptic curves and power-free values of binary forms	1995	C. L. Stewart J. Top	4
+ PDF Chat	The distribution of the Tamagawa ratio in the family of elliptic curves with a two-torsion point	2014	Zev Klagsbrun Robert J. Lemke Oliver	4
+	Uniform bounds for rational points on cubic hypersurfaces	2015	Per Salberger	4
+ PDF Chat	Counting rational points on projective varieties	2023	Per Salberger	4
+ PDF Chat	The density of rational points on cubic surfaces	1997	D. R. Heath‐Brown	4
+	On the 4-rank of class groups of quadratic number fields	2006	Étienne Fouvry Jürgen Klüners	4
+ PDF Chat	Higher composition laws I: A new view on Gauss composition, and quadratic generalizations	2004	Manjul Bhargava	4
+ PDF Chat	Power-free values of polynomials	2011	T. D. Browning	4
+	Binary Quadratic Forms: Classical Theory and Modern Computations	1989	Duncan A. Buell	3
+ PDF Chat	Binary quartic forms with bounded invariants and small Galois groups	2019	Cindy Tsang Stanley Yao Xiao	3
+	On Another Sieve Method and the Numbers that are a Sum of Two <i>h</i> th Powers	1981	C. Hooley	3
+ PDF Chat	On the number of cubic orders of bounded discriminant having automorphism group <i>C</i><sub>3</sub>, and related problems	2014	Manjul Bhargava Ariel Shnidman	3
+ PDF Chat	Quartic Rings Associated to Binary Quartic Forms	2011	Melanie Matchett Wood	3
+ PDF Chat	Bounded Rational Points on Curves	2014	Miguel N. Walsh	3
+ PDF Chat	Primes represented by x3+2y3	2001	D. R. Heath‐Brown	3
+	The number of quartic $D_4$-fields ordered by conductor	2017	Salim Ali Altuğ Arul Shankar Ila Varma Kevin H. Wilson	3
+ PDF Chat	The square-free sieve and the rank of elliptic curves	1991	Fernando Gouvêa Barry Mazur	3
+ PDF Chat	On the square-free sieve	2004	H. A. Helfgott	3
+ PDF Chat	Klein forms and the generalized superelliptic equation	2013	Michael A. Bennett Sander R. Dahmen	3
+ PDF Chat	The density of discriminants of quartic rings and fields	2005	Manjul Bhargava	3
+	The Average Measure of Quadratic Forms With Given Determinant and Signature	1944	Carl Ludwig Siegel	3
+ PDF Chat	On the density of rational and integral points on algebraic varieties	2007	Per Salberger	3
+	Power Free Values of Polynomials III	1980	M. N. Huxley M. Nair	3
+	Primes Represented by Binary Cubic Forms	2002	D. R. Heath‐Brown B. Z. Moroz	3
+ PDF Chat	The representation of integers by binary additive forms	1998	Michael A. Bennett Neil Dummigan Trevor D. Wooley	3
+ PDF Chat	Friable values of binary forms	2012	Antal Balog Valentin Blomer Cécile Dartyge Gérald Tenenbaum	3
+ PDF Chat	Counting rational points on hypersurfaces	2005	T. D. Browning D. R. Heath‐Brown	3
+ PDF Chat	Higher composition laws III: The parametrization of quartic rings	2004	Manjul Bhargava	3
+	The Theory of Irrationalities of the Third Degree	2009	B. Delone D. K. Faddeev	3
+	On binary cubic forms.	1967	C. Hooley	3
+	The practical computation of areas associated with binary quartic forms	1997	Michael A. Bean	3