MATHEMATICAL OUTPUT OF WILLIAM CHEN
### Monographs and Books:

### Edited Books:

### Edited Special Issues:

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

### Papers in Preparation:

### Papers in Refereed Journals:

### Papers in Conference Proceedings:

### Chapters in Books:

### Other Papers:

### Lecture Notes:

- (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).

- (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). >> >>

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

- (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) >>

- (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.

- 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. ThÃ©or. Nombres Bordeaux***35**(2023), 511-542. >> >>

- 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). >>

- (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). >>

- 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. >>

*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). >>