| 2006 |
|
On Q-derived polynomials,
Rocky Mountain Journal of Mathematics 36(5),
1705-1713. |
| 2003 |
|
(with N. Tzanakis) Computing all integer solutions of a
genus 1 equation, Mathematics
of Computation 72, 1935-1946.
The very large X(u,v) and Y(u,v) of the degree 9 example are
contained in largeXY.pdf. |
| 2000 |
|
(with N. Tzanakis) Computing All Integer Solutions of a General Elliptic
Equation, In: Algorithmic Number Theory (ed. Wieb Bosma), Proceedings of the 4th
International Symposium, ANTS-IV, Leiden, July 2000, Lecture Notes in Computer
Science 1838, Springer, 551-561. |
| 1999 |
|
(with B.M.M. de Weger) Elliptic binomial diophantine equations, Mathematics
of Computation 68, 1257-1281. |
| 1999 |
|
(with B.M.M. de Weger) Solving elliptic diophantine equations: the general
cubic case, Acta Arithmetica LXXXVII.4, 339-365. |
| 1999 |
|
(with N. Tzanakis) On the elliptic logarithm method for elliptic
diophantine equations: Reflections and an improvement, Experimental Mathematics
8:2, 135-149.
Additional material comprising tables of integer points are contained in st99pts.pdf or st99pts.ps. |
| 1999 |
|
(with B.M.M. de Weger) On integral zeroes of binary Krawtchouk
polynomials, Nieuw Archief v. Wiskunde, Vierde Serie 17(2),
175-186. |
| 1997 |
|
(with A. Bremner and N. Tzanakis) On the sum of consecutive squares, Journal
of Number Theory 62, 39-70. |
| 1996 |
|
(with B.M.M. de Weger) On a quartic diophantine equation, Proceedings
of the Edinburgh Mathematical Society 39, 97-114. |
| 1995 |
|
On the sum of consecutive cubes being a perfect square, Compositio
Mathematica 97, 295-307. |
| 1994 |
|
(with N. Tzanakis) Solving elliptic diophantine equations by estimating
linear forms in elliptic logarithms, Acta Arithmetica LXVII.2,
177-196. |
| 1994 |
|
(with J. Top) On the equation y2=(x+p)(x2+
p2),
Rocky Mountain Journal of Mathematics 24(3), 1135-1161. |
| 1994 |
|
(with B.M.M. deWeger) On elliptic diophantine equations that defy Thue's
method. The case of the Ochoa curve, Experimental Mathematics 3,
209-220. |
| 1994 |
|
(with P. Fischer) Some interesting logarithmic inequalities and a problem
of Polya and Szego, Nieuw Archief voor Wiskunde (4th Series) 12,
119-124. |
| 1992 |
|
Improvement of Nakamula's upper bound for the absolute discriminant of a
sextic number field with two real conjugates, Mathematics of Computation 59,
203-211. |
| 1991 |
|
On Thue equations associated with certain quartic number fields, In: Computational
Number Theory (eds. Attila PethHo, Michael E. Pohst, Hugh C. Williams, Horst Günter
Zimmer). Proceedings of the Colloquium on Computational Number Theory, Debrecen (Hungary),
1989, Walter de Gruyter, Berlin New York, 313-319. |
| 1989 |
|
On diophantine equations of type x4- 2ax2y2-by4=1,
Proceedings NATO-Advanced Study Institute on Number Theory and Applications (ed. R. Mollin). Banff 1988, 547-553. |
| 1989 |
|
On quartic Thue equations with trivial solutions, Mathematics of
Computation 52, 175-187. |
| 1988 |
|
Brocard points, circulant matrices, and Descartes' folium, Mathematics
Magazine 61, 172-187. |
| 1988 |
|
(with N. Tzanakis) On the application of Skolem's p-adic method to the
solution of Thue equations, Journal of Number Theory 29,
166-195. |
| 1986 |
|
An inequality for Yff's analogue of the Brocard angle of a plane triangle,
Nieuw Archief voor Wiskunde (4th Series) 4, 33-45. |
| 1984 |
|
How to solve a diophantine equation. A number theoretic excursion, American
Mathematical Monthly 91, 385-392. |
| 1984 |
|
(with H.J.T. Hoogland) Brocardian geometry revisited, or some remarkable
inequalities, Nieuw Archief voor Wiskunde (4th Series) 2,
281-310. |
| 1983 |
|
Reduction of elliptic curves over imaginary quadratic number fields, Pacific
Journal of Mathematics 108, 451-463. |
| 1983 |
|
Approximations of the eigenvalues of the covariance matrix of a first
order autoregressive process, Journal of Econometrics 22,
269-279. |
| 1982 |
|
(with R. Tijdeman) Diophantine equations (including an appendix by P.L.
Cijsouw, A. Korlaar and R. Tijdeman). In: Computational Methods in Number Theory Part II
(eds: H.W. Lenstra Jr. and R. Tijdeman), Mathematical Centre Tracts 155,
321-369. |
| 1981 |
|
On the diophantine equation (2y2-3)2= x2(3x2-2)
in connection with the existence of non-trivial tight 4-designs, Indagationes
Mathematicae 43, 353-358. |
| 1980 |
|
The diophantine equation (x2+y)(x+y2)= N(x-y)3,
Simon Stevin 54, 151-163. |
| 1979 |
|
A class of diophantine equations connected with certain elliptic curves
over Q(√-13)Compositio Mathematica 38,
329-346. |
| 1979 |
|
Application of non-linear programming to plane geometry, Elemente der
Mathematik 34, 1-8. |
| 1978 |
|
Aspects of elliptic curves: an introduction, Nieuw Archief voor
Wiskunde (3rd Series) 26, 371-413. |
| 1977 |
|
On a diophantine equation of E. Bombieri, Indagationes Mathematicae
39, 131-139. |
1976 |
|
On the diophantine equation x3-Dy2=1, Nieuw
Archief voor Wiskunde (3rd Series) 24, 231-254. |
Over a period of more than two decades I wrote many reports for the Report Series of
the Econometric Institute. Most of these, in some form or other, were published in
journals. The reports below have not (yet) been published in any other form.
| 9069/B |
|
Improvement of Nakamula's upper bound for the absolute discriminant of a sextic number
field with two real conjugates, 17 pages. The appendix gives the details of the symbolic
computations of the 1992 publication in Mathematics of Computation. |
| 8607/B |
|
(with N. Tzanakis) On certain norm form equations associated with a totally real
biquadratic field, 38 pages. |
| 8216/M |
|
On the shape of units in certain biquadratic number fields, 8 pages. |
| 8113/M |
|
(with N.M. Stephens) The torsion group of elliptic curves over quadratic fields, 8
pages. |
| 8014/M |
|
Factorization methods for solving diophantine equations, 27 pages. |
| 7701/M |
|
Triangular-Square-Pentagonal numbers, 8 pages. |
| 7209 |
|
Elliptic curves over imaginary quadratic number fields, 16 pages. |
The following papers appeared in the Dutch language or were not subjected to any
refereeing system.
| 1993 |
|
(in Dutch) Maple en Mathematica op de PC 1,2, Erasmus On Line 1(2)
en 1(3), 21-25, 18-20, 38. |
| 1990 |
|
(in Dutch) Computer Algebra: Maple of Mathematica?, MacPROF 31,
10-17. |
| 1989 |
|
(in Dutch) Expressionist versie 2.0, MacPROF 25, 28-34. |
| 1988 |
|
A mathematician's personal view, The Web, Webster University Leiden, 2-4. |
| 1984 |
|
(in Dutch) Kleinste kwadraten methoden, CWI Syllabus 1, Vakantiecursus : Hewet-Plus
Wiskunde, Mathematisch Centrum Amsterdam, 43-61. |
| 1980 |
|
(in Dutch) De magische kubus, Sectief (Bulletin
of the Econometric Institute of the EUR) nrs. 26 (1980), 27 and 29 (1981),
15 pages. |
| 1980 |
|
(in Dutch) Diophantische vergelijkingen (constructieve algebraïsche methoden), In: Number
Theory and Computers, Mathematisch Centrum Amsterdam, 239-260. |
| 1976 |
|
(in Dutch) Een interessante rij, Nieuw Tijdschrift voor Wiskunde 63
268-274. |
| 1974 |
|
(in Dutch) Identiteiten voor de som, de som van de kwadraten, en de som van derde
machten van natuurlijke getallen, Nieuw Tijdschrift voor Wiskunde 62,
94-100. |
| 1972 |
|
(in Dutch) Pythagoras met een nevenvoorwaarde, Euclides 47,
217-220. |
| 1970 |
|
Elliptic curves over Q(√-2)
with conductor N=(√-2)n,
Manchester University, 50 pages. |
| 1970 |
|
Essay on the history of the diophantine equation y2+k= x3,
Manchester University, 59 pages. |
This book introduces Maple in a rather
special way; namely, it shows how a computer algebra system most naturally fits into a
mathematical oriented work environment.