Books

Papers in Journals

2015
On the shape of a violin, Mathematics Magazine 88(4), 247-259. Data points are contained in Stradpoints.
2012
(with W.Y. Pong) Diophantine Equations of Matching Games II, Acta Arithmetica 151 (3), 311-323.
2006
On Q-derived polynomials, Rocky Mountain Journal of Mathematics 36(5), 1705-1713.
2004
(with B.M.M. de Weger) On integral zeroes of binary Krawtchouk polynomials. In: N. Virchenko, I. Katchanovski, V. Haidey, R. Andrushkiw & R. Voronka (Eds.). Development of the mathematical ideas of Mykhailo Kravchuk (Krawtchouk). New York NY, USA. Shevchenko Scientific Society, 623-633.
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.

Reports

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.

Other Publications

The following papers appeared in the Dutch language or were not subjected to any refereeing system.

2007
(in Dutch) De Viola da Gamba en de Gulden Snede, CMB Puurs (BE), 11 pages.
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.