Mathematical Output

MATHEMATICAL OUTPUT OF WILLIAM CHEN

Monographs and Books:

(with J. Beck) Irregularities of Distribution, xiv + 294 pp. (Cambridge Tracts in Mathematics 89, Cambridge University Press, 1987; paperback reprint, 2008). >>
(with J. Beck and Y. Yang) Non-Integrable Dynamics: Time-Quantitative Results, xv + 384 pp. (World Scientific, 2024).
(with J. Beck and Y. Yang) Non-Integrable Flat Dynamical Systems, approx. 400 pp. (World Scientific, in preparation, to submit in March 2024).
(with J. Beck) Discrepancy Theory, approx. 300 pp. (World Scientific, in preparation, to submit in January 2025).

Edited Books:

(with W.T. Gowers, H. Halberstam, W.M. Schmidt and R.C. Vaughan) Analytic Number Theory: Essays in Honour of Klaus Roth (Cambridge University Press, 2009). >> >>
(with A. Srivastav and G. Travaglini) A Panorama of Discrepancy Theory (Lecture Notes in Mathematics 2107, Springer Verlag, 2014). >> >>

Edited Special Issues:

(with R.C. Vaughan) In Memoriam: Klaus Friedrich Roth (Mathematika, volume 63, issue 3, 2017). >>

Recent Preprints (from 2022) (see also others under Papers in Refereed Journals):

(with J. Beck) Time-quantitative density of non-integrable systems (28 pages) (preprint on arxiv.org). >>
(with J. Beck) Superdensity and super-micro-uniformity in non-integrable flat systems (18 pages) (preprint on arxiv.org). >>
(with J. Beck) Super-fast spreading of billiard orbits in rational polygons and geodesics on translation surfaces (32 pages) (preprint on arxiv.org) >>

Papers in Preparation:

(with J. Beck and Y. Yang) Billiards in polyhedra: a method to convert 2-dimensional uniformity to 3-dimensional uniformity.
(with J. Beck and Y. Yang) Uniformity of geodesic flow in non-integrable 3-manifolds.
(with J. Beck and Y. Yang) Uniformity in cube-covering systems.
(with J. Beck and Y. Yang) Irreversible and dissipative systems.

Papers in Refereed Journals:

On the error term of the prime number theorem and the difference between the number of primes in the residue classes modulo 4, J. London Math. Soc., 23 (1981), 24-40. >>
On irregularities of distribution, Mathematika, 27 (1980), 153-170. >>
On irregularities of distribution II, Quart. J. Math. Oxford, 34 (1983), 257-279. >>
On irregularities of distribution and approximate evaluation of certain functions, Quart. J. Math. Oxford, 36 (1985), 173-182. >>
(with J. Beck) Note on irregularities of distribution, Mathematika, 33 (1986), 148-163. >>
(with J. Beck) Note on irregularities of distribution II, Proc. London Math. Soc., 61 (1990), 251-272. >>
On irregularities of distribution III, J. Austral. Math. Soc. (A), 60 (1996), 228-244. >> >>
(with J. Beck) Irregularities of point distribution relative to half planes I, Mathematika, 40 (1993), 102-126. >> >>
(with J. Beck) Irregularities of point distribution relative to convex polygons II, Mathematika, 40 (1993), 127-136. >> >>
(with J. Beck) Irregularities of point distribution relative to convex polygons III, J. London Math. Soc., 56 (1997), 222-230. >> >>
(with V.F. Lev) Discrepancy of weighted matrix nets, Acta Arith., 85 (1998), 141-156. >> >>
On irregularities of distribution IV, J. Number Theory, 80 (2000), 44-59. >> >>
(with M.M. Skriganov) Explicit constructions in the classical mean squares problem in irregularities of point distribution, J. reine angew. Math. (Crelle), 545 (2002), 67-95. >> >>
(with G. Travaglini) Discrepancy with respect to convex polygons, J. Complexity, 23 (2007), 662-672. >> >>
(with G. Travaglini) Deterministic and probabilistic discrepancies, Ark. Mat., 47 (2009), 273-293. >> >>
(with L. Brandolini, G. Gigante and G. Travaglini) Discrepancy for randomized Riemann sums, Proc. American Math. Soc., 137 (2009), 3187-3196. >> >>
(with G. Travaglini) An L1 estimate for half space discrepancy, Acta Arith., 146 (2011), 203-214. >> >>
Davenport's theorem in geometric discrepancy theory, Internat. J. Number Theory, 11 (2015), 1437-1449. >> >>
(with L. Brandolini, L. Colzani, G. Gigante and G. Travaglini) Discrepancy and numerical integration on metric measure spaces, J. Geom. Anal., 29 (2019), 328-369. >> >>
(with J. Beck and Y. Yang) Quantitative behavior of non-integrable systems III, Acta Math. Hungar., 166 (2022), 254-372. (version on arxiv.org) >> >>
(with J. Beck and Y. Yang) Quantitative behavior of non-integrable systems IV, Acta Math. Hungar., 167 (2022), 1-160. >> >>
(with J. Beck and Y. Yang) New Kronecker-Weyl type equidistribution results and diophantine approximation, Eur. J. Math. 9 (2023), article 38 (87 pages). >> >>
(with J. Beck) Generalization of a density theorem of Khinchin and diophantine approximation, J. Théor. Nombres Bordeaux 35 (2023), 511-542. >> >>

Papers in Conference Proceedings:

Irregularities of point distribution in unit cubes, Journées Arithmétiques 1980, pp. 232-236 (London Mathematical Society Lecture Note Series 56, Cambridge University Press, 1982).
On irregularities of distribution and approximate evaluation of certain functions II, Analytic Number Theory and Diophantine Problems 1984, pp. 75-86 (Progress in Mathematics 70, Birkhäuser Verlag, 1987).
(with J. Beck) Irregularities of point distribution relative to convex polygons, Irregularities of Partitions Fertöd 1986, pp. 1-22 (Algorithms and Combinatorics 8, Springer Verlag, 1989). >>
Fourier techniques in the theory of irregularities of point distribution, Fourier Analysis and Convexity, pp. 59-82 (Applied and Numerical Harmonic Analysis, Birkhäuser, 2004). >> >>
(with M.M. Skriganov) Orthogonality and digit shifts in the classical mean squares problems in irregularities of point distribution, Diophantine Approximation: Festschrift for Wolfgang Schmidt, pp. 141-159 (Developments in Mathematics 16, Springer Verlag, 2008). >> >>
Upper bounds in discrepancy theory, Monte Carlo and Quasi-Monte Carlo Methods 2010, pp. 23-41 (Springer Proceedings in Mathematics and Statistics 23, Springer Verlag, 2012). >> >>
Results and problems old and new in discrepancy theory, Discrepancy Theory, pp. 21-42 (Radon Series on Computational and Applied Mathematics, de Gruyter, 2020). >>

Chapters in Books:

(with J.R. Alexander and J. Beck) Geometric discrepancy theory and uniform distribution, Handbook of Discrete and Computational Geometry, pp. 185-207 (CRC Press, 1997).
(with J.R. Alexander and J. Beck) Geometric discrepancy theory and uniform distribution, Handbook of Discrete and Computational Geometry, 2nd edition, pp. 279-304 (CRC Press, 2004).
(with G. Travaglini) Some of Roth's ideas in discrepancy theory, Analytic Number Theory: Essays in Honour of Klaus Roth, pp. 150-163 (Cambridge University Press, 2009). >> >>
(with M.M. Skriganov) Upper bounds in classical discrepancy theory, A Panorama of Discrepancy Theory, pp. 3-69 (Lecture Notes in Mathematics 2107, Springer Verlag, 2014). >> >>
(with J.R. Alexander and J. Beck) Geometric discrepancy theory and uniform distribution, Handbook of Discrete and Computational Geometry, 3rd edition, pp. 331-357 (CRC Press, 2018). >>

Other Papers:

Upper bounds in irregularities of distribution (Macquarie Mathematics Report, 1992). >>
(with M.M. Skriganov) Davenport's theorem in the theory of irregularities of point distribution, Zapiski Nauch. Sem. POMI, 269 (2000), 339-353; reprinted in J. Math. Sci., 115 (2003), 2076-2084. >>
(with K. Matthews and R. Street) Obituary: Peter Pleasants, Gazette Aust. Math. Soc., 35 (2008), 162-165. >>
(with R.C. Vaughan) Obituary: Klaus Friedrich Roth, Biogr. Mem. Fellows R. Soc., 63 (2017), 487-525. >>
(with R.C. Vaughan) Obituary: Klaus Friedrich Roth, Bull. London Math. Soc., 50 (2018), 529-560. >>

Lecture Notes:

A View of Mathematics (web edition, 2019). >>
(with X.T. Duong) Elementary Mathematics, 148 pp. (web edition, 2000). >>
Miscellaneous Topics in First Year Mathematics, 56 pp. (web edition, 2008). >>
First Year Calculus, 281 pp. (web edition, 2008). >>
Discrete Mathematics, 201 pp. (web edition, 2008). >>
Linear Algebra, 237 pp. (web edition, 2008). >>
Multivariable and Vector Analysis, 164 pp. (web edition, 2008). >>
Introduction to Complex Analysis, 172 pp. (web edition, 2008). >>
Fundamentals of Analysis, 100 pp. (web edition, 2008). >>
Linear Functional Analysis, 91 pp. (web edition, 2008). >>
Introduction to Lebesgue Integration, 77 pp. (web edition, 2008). >>
Introduction to Ordinary Differential Equations, 1-63 (web edition, 2013). >>
Introduction to Abstract Algebraic Structures, 1-79 (web edition, 2013). >>
Fourier Series and Transforms, 1-76 (web edition, 2013). >>
Elementary Number Theory, 1-51 (web edition, 2013). >>
Distribution of Prime Numbers, 1-76 (web edition, 2013). >>
Introduction to Algebraic Numbers, 1-48 (web edition, 2013). >>
Hardy-Littlewood Method, 1-42 (web edition, 2013). >>
Lectures on Irregularities of Point Distribution, 63 pp. (web edition, 2000). >>
Lectures on Discrepancy Theory, 99 pp. (web edition, 2012). >>