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).
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, to appear). (list of contents)
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. (PDF version)
- (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. (PDF version)
- (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. (PDF
version)
- (with G. Travaglini) "Discrepancy
with respect to convex polygons", J. Complexity,
23 (2007), 662-672. (PDF
version)
- (with G. Travaglini) "Deterministic
and probabilistic discrepancies", Ark. Mat. (to appear).
(PDF version)
- (with L. Brandolini, G. Gigante and
G. Travaglini) "Discrepancy for randomized Riemann sums"
(manuscript). (PDF version)
- (with G. Travaglini) "An L1 estimate
for half space discrepancy" (manuscript). (PDF version)
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). (PDF
version)
- (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). (PDF
version)
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). (PDF version)
- (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). (PDF
version)
- (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, to appear). (PDF version)
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.
(PDF version)
Lecture Notes:
- (with X.T. Duong) Elementary
Mathematics, 148 pp. (web edition, 2000).
- First
Year Calculus, 281 pp. (web
edition, 2008).
- Discrete
Mathematics, 201 pp. (web
edition, 2008).
- Linear
Algebra, 237 pp. (web edition,
2008).
- Miscellaneous
Topics in First Year Mathematics,
56 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).
- Elementary
Number Theory, 69 pp. (web
edition, 2003).
- Distribution
of Prime Numbers, 81 pp.
(web edition, 2003).
- Lectures
on Irregularities of Point Distribution,
63 pp. (web edition, 2000).