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, approx. 400 pp. (World Scientific, in preparation, to submit in January 2023).
• (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 (preprint on arxiv.org, 27 pp). >>
• (with J. Beck) Superdensity and super-micro-uniformity in non-inregrable flat systems (preprint on arxiv.org, 19 pp). >>
• (with J. Beck) Super-fast spreading of billiard orbits in rational polygons and geodesics on translation surfaces (preprint on arxiv.org, 32 pp.) >>

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 (accepted) (preprint on arxiv.org, 24 pp). >>

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). >>