William Chen

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All published works

Action	Title	Year	Authors
+ PDF Chat	A note on the Kronecker--Weyl equidistribution theorem	2024	József Beck William Chen Yaping Yang
+ PDF Chat	Irreversible and dissipative systems	2024	James L. Beck William Chen Yihao Yang
+ PDF Chat	Generalization of a density theorem of Khinchin and diophantine approximation	2023	József Beck William Chen
+ PDF Chat	A Comparative Study on E-Branchformer vs Conformer in Speech Recognition, Translation, and Understanding Tasks	2023	Yifan Peng Kwangyoun Kim Felix Wu Brian Yan Siddhant Arora William Chen Jiyang Tang Suwon Shon Prashant Sridhar Shinji Watanabe
+ PDF Chat	New Kronecker–Weyl type equidistribution results and Diophantine approximation	2023	József Beck William Chen Yuxuan Yang
+	A Comparative Study on E-Branchformer vs Conformer in Speech Recognition, Translation, and Understanding Tasks	2023	Yifan Peng Kwangyoun Kim Felix F. Wu Brian Yan Siddhant Arora William Chen Jiyang Tang Suwon Shon Prashant Sridhar Shinji Watanabe
+ PDF Chat	Quantitative Behavior Of Non-Integrable Systems. IV	2022	József Beck William Chen Yusheng Yang
+ PDF Chat	RETRACTED - THE KRONECKER–WEYL EQUIDISTRIBUTION THEOREM AND GEODESICS IN 3-MANIFOLDS	2022	James V. Beck William Chen
+	Uniformity of 3-dimensional billiards	2020	József Beck William Chen
+	Billiard orbits and geodesics in non-integrable flat dynamical systems (part 1)	2020	William Chen
+	The Kronecker-Weyl equidistribution theorem and geodesics in 3-manifolds	2020	József Beck William Chen
+ PDF Chat	Klaus Friedrich Roth, 1925-2015	2018	William Chen R. C. Vaughan
+ PDF Chat	Discrepancy and Numerical Integration on Metric Measure Spaces	2018	Luca Brandolini William Chen Leonardo Colzani Giacomo Gigante Giancarlo Travaglini
+ PDF Chat	Handbook of Discrete and Computational Geometry, Third Edition	2017	J. Ralph Alexander József Beck William Chen
+ PDF Chat	Klaus Friedrich Roth. 29 October 1925 — 10 November 2015	2017	William Chen R. C. Vaughan
+ PDF Chat	IN MEMORIAM KLAUS FRIEDRICH ROTH 1925–2015	2017	William Chen R. C. Vaughan
+	On Finding Geodesic Equation of Two Parameters Extreme Value and Related Six Distribution	2016	William Chen
+	Damped Infinite Energy Solutions of the 3D Euler and Boussinesq Equations	2016	William Chen Alejandro Sarria
+	Davenport's theorem in geometric discrepancy theory	2015	William Chen
+	Upper Bounds in Classical Discrepancy Theory	2014	William Chen M. M. Skriganov
+	A Panorama of Discrepancy Theory	2014	William Chen Anand Srivastav Giancarlo Travaglini
+	Discrepancy and numerical integration in Sobolev spaces on metric measure spaces	2013	Luca Brandolini William Chen Leonardo Colzani Giacomo Gigante Giancarlo Travaglini
+	Upper Bounds in Discrepancy Theory	2012	William Chen
+ PDF Chat	An L<sup>1</sup>estimate for half-space discrepancy	2010	William Chen Giancarlo Travaglini
+	An L^1 estimate for half-space discrepancy	2010	William Chen Giancarlo Travaglini
+	An L^1 estimate for half-space discrepancy	2010	William Chen Giancarlo Travaglini
+ PDF Chat	Discrepancy for randomized Riemann sums	2009	Luca Brandolini William Chen Giacomo Gigante Giancarlo Travaglini
+	An analogue of the Gallai–Edmonds Structure Theorem for non-zero roots of the matching polynomial	2009	Cheng Yeaw Ku William Chen
+ PDF Chat	Deterministic and probabilistic discrepancies	2008	William Chen Giancarlo Travaglini
+	Orthogonality and Digit Shifts in the Classical Mean Squares Problem in Irregularities of Point Distribution	2008	William Chen M. M. Skriganov
+	The limiting distribution of the coefficients of the 𝑞-Catalan numbers	2008	William Chen Carol Wang Larry X. W. Wang
+	An Analogue of the Gallai-Edmonds Structure Theorem for Nonzero Roots of the Matching Polynomial	2008	Cheng Yeaw Ku William Chen
+	Discrepancy with respect to convex polygons	2007	William Chen Giancarlo Travaglini
+	Concrete and abstract structure of the sandpile group for thick trees with loops	2007	William Chen Travis Schedler
+	Semi-finite forms of bilateral basic hypergeometric series	2005	William Chen Amy M. Fu
+	Discrepancy Theory and Its Applications	2004	Bernard Chazelle William Chen Anand Srivastav
+	Geometric Discrepancy Theory Anduniform Distribution	2004	J Ralph Alexander József Beck William Chen
+	Fourier Techniques in the Theory of Irregularities of Point Distribution	2004	William Chen
+	None	2003	William Chen M. M. Skriganov
+	Explicit constructions in the classical mean squares problem in irregularities of point distribution	2002	William Chen M. M. Skriganov
+	On Irregularities of Distribution IV	2000	William Chen
+	Counterexamples to Knaster's conjecture	1998	William Chen
+ PDF Chat	Discrepancy of weighted matrix nets	1998	William Chen Vsevolod F. Lev
+	Irregularities of Point Distribution Relative to Convex Polygons III	1997	József Beck William Chen
+ PDF Chat	On irregularities of distribution III	1996	William Chen
+ PDF Chat	Restricted routing and wide diameter of the cycle prefix network	1995	William Chen Vance Faber Emanuel Knill
+	Irregularities of point distribution relative to half‐planes I	1993	József Beck William Chen
+	Irregularities of point distribution relative to convex polygons II	1993	József Beck William Chen
+	Note on Irregularities of Distribution II	1990	József Beck William Chen
+	Irregularities of Distribution	1987	József Beck William Chen
+	More upper bounds	1987	József Beck William Chen
+	Lower bounds – Roth's method	1987	József Beck William Chen
+	Note on irregularities of distribution	1986	József Beck William Chen
+	ON IRREGULARITIES OF DISTRIBUTION AND APPROXIMATE EVALUATION OF CERTAIN FUNCTIONS	1985	William Chen
+	ON IRREGULARITIES OF DISTRIBUTION II	1983	William Chen
+	On the Error Term of the Prime Number Theorem and the Difference between the Number of Primes in the Residue Classes Modulo 4	1981	William Chen
+	On irregularities of distribution	1980	William Chen

Common Coauthors

Coauthor	Papers Together
József Beck	16
Giancarlo Travaglini	9
M. M. Skriganov	4
Giacomo Gigante	3
Luca Brandolini	3
R. C. Vaughan	3
Jiyang Tang	2
Shinji Watanabe	2
Anand Srivastav	2
Leonardo Colzani	2
Cheng Yeaw Ku	2
Suwon Shon	2
Prashant Sridhar	2
Yifan Peng	2
Siddhant Arora	2
Kwangyoun Kim	2
Yusheng Yang	1
Yuxuan Yang	1
J. Ralph Alexander	1
Brian Yan	1
Yihao Yang	1
Felix F. Wu	1
Vsevolod F. Lev	1
Brian Yan	1
James L. Beck	1
James V. Beck	1
Emanuel Knill	1
Bernard Chazelle	1
Vance Faber	1
Amy M. Fu	1
Alejandro Sarria	1
Felix Wu	1
Travis Schedler	1
Larry X. W. Wang	1
Yaping Yang	1
J Ralph Alexander	1
Carol Wang	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Note on irregularities of distribution	1956	H. Davenport	20
+	On irregularities of distribution	1954	K. F. Roth	19
+ PDF Chat	On irregularities of distribution, III	1979	K. Roth	19
+ PDF Chat	Irregularities of distribution. I	1987	József Beck	16
+	Note on Irregularities of Distribution II	1990	József Beck William Chen	14
+	Irregularities of Distribution	1987	József Beck William Chen	13
+	On irregularities of distribution	1980	William Chen	13
+	On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals	1960	John H. Halton	11
+ PDF Chat	On irregularities of distribution, IV	1980	K. Roth	11
+	ON IRREGULARITIES OF DISTRIBUTION II	1983	William Chen	9
+	The extreme and L2 discrepancies of some plane sets	1969	John H. Halton S. K. Zaremba	8
+	Irregularities of point distribution relative to half‐planes I	1993	József Beck William Chen	8
+ PDF Chat	Irregularities of distribution, VII	1972	Wolfgang Schmidt	7
+	Explicit constructions in the classical mean squares problem in irregularities of point distribution	2002	William Chen M. M. Skriganov	7
+	Irregularities of Point Distribution Relative to Convex Polygons III	1997	József Beck William Chen	7
+	Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis	1994	Hugh L. Montgomery	6
+ PDF Chat	Tight upper bounds for the discrepancy of half-spaces	1995	Jiřı́ Matoušek	6
+	Irregularities of Distribution, II	1988	József Beck	6
+	On a problem of K.F. Roth concerning irregularities of point distribution	1983	József Beck	6
+ PDF Chat	Average decay of Fourier transforms and integer points in polyhedra	1997	Luca Brandolini Leonardo Colzani Giancarlo Travaglini	6
+	Geometric methods in the study of irregularities of distribution	1990	Ralph Alexander	6
+	Note on irregularities of distribution	1986	József Beck William Chen	5
+	A note on Diophantine approximation (II)	1964	H. Davenport	5
+ PDF Chat	Deterministic and probabilistic discrepancies	2008	William Chen Giancarlo Travaglini	5
+	A Course in Probability Theory	1974	Kai Lai Chung	5
+ PDF Chat	On the Walsh functions	1949	N. J. Fine	5
+ PDF Chat	Irregularities for distribution IX	1975	Wolfgang Schmidt	5
+	On the Small Ball Inequality in all dimensions	2007	Dmitriy Bilyk Michael T. Lacey Armen Vagharshakyan	4
+	Number Theory and Algebra	1995	Rajeev Motwani Prabhakar Raghavan	4
+	Quantitative behavior of non-integrable systems. II	2020	József Beck M. Donders Yusheng Yang	4
+ PDF Chat	Certain Groups of Orthonormal Step Functions	1957	J. J. Price	4
+ PDF Chat	Boshernitzan's criterion for unique ergodicity of an interval exchange transformation	1987	William A. Veech	4
+	Geometric Discrepancy	1999	Jiřı́ Matoušek	4
+	Lectures on irregularities of distribution	1977	Wolfgang M. Schmidt T. N. Shorey	4
+ PDF Chat	Billiards on almost integrable polyhedral surfaces	1984	Eugène Gutkin	4
+	MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS	1960	J. M. Hammersley	4
+	An Introduction to Diophantine Approximation.	1958	John C. Brixey J. W. S. Cassels	3
+ PDF Chat	Some upper bounds in the theory of irregularities of distribution	1984	József Beck	3
+	Coding Theory and Uniform Distributions	1999	M. M. Skriganov	3
+ PDF Chat	On irregularities of distribution III	1996	William Chen	3
+	Fourier Techniques in the Theory of Irregularities of Point Distribution	2004	William Chen	3
+	On irregularities of distribution, II	1976	K. F. Roth	3
+	Recurrence in Ergodic Theory and Combinatorial Number Theory	1981	Harry Furstenberg	3
+	Irregularities of distribution. IV	1969	Wolfgang M. Schmidt	3
+	An Introduction to Veech Surfaces	2006	Pascal Hubert Thomas Schmidt	3
+	Balanced two-colorings of finite sets in the square I	1981	József Beck	3
+	The billiard in a regular polygon	1992	William A. Veech	3
+	Irregularities of point distribution relative to convex polygons II	1993	József Beck William Chen	3
+ PDF Chat	Some problems of Diophantine approximation: The lattice-points of a right-angled triangle. (Second memoir.)	1922	G. H. Hardy J. E. Littlewood	3
+	Harmonic analysis on totally disconnected groups and irregularities of point distributions	2006	M. M. Skriganov	3