Ronald M. van Luijk
Theses
Papers
Published:
- Nontrivial elements of Sha explained through K3 surfaces and
accompanying files, Math. Comp. 78 (2009), 441-483. (joint work with Adam Logan, also available at arXiv:0706.0541).
- Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces and in PDF, Mathematical Intelligencer, Vol. 30, No. 4 (2008), 4--10 (joint work with Robin Hartshorne, also vailable at arXiv:math.NT/0606700).
- The diameter of the circumcircle of a Heron
triangle and in PDF, Elemente der Mathematik, Vol. 63, Issue 3 (2008), p. 118-121.
- K3 surfaces with Picard number one and infinitely many rational points and in PDF, Algebra and Number Theory,
Vol. 1, No. 1 (2007), 1-15.
- K3 surfaces with Picard number
three and canonical vector heights
and in PDF, Mathematics of Computation, Volume 76 (2007), 1493-1498
(joint work with Arthur Baragar, different version available at arXiv:math.AG/0602166 ).
- An elliptic K3 surface associated
to Heron triangles and in
PDF, Journal of Number Theory, Volume 123 (2007), 92-119, also available at
arXiv:math.AG/0411606).
- A K3 surface
associated to certain integral matrices with integral
eigenvalues and in PDF
Canadian Mathematical Bulletin,
Volume 49 (4), 2006, 560-577, also available at
arXiv:math.AG/0411600).
- Quartic K3 surfaces without nontrivial automorphisms and in
PDF, Mathematical Research Letters (MRL), Volume 13 (2006), Issue 3, 423-439, also available at
arXiv:math.AG/0511542).
- A
linear algebra exercise, with F. Beukers and R. Vidunas, Nieuw
Archief voor Wiskunde (NAW), Juni 2002, 139-140.
Submitted:
Slides
The slides I used for some presentations:
Pictures
Various
- Wiskunde Olympiade with Jan van de Craats and Thijs Notenboom, Nieuw Archief voor Wiskunde, December 2000, 448-450 (Dutch).
- Hex, dots and boxes with Sander van Rijnswou, Nieuw Archief voor Wiskunde, December 2001, 358-361 (Dutch).
- IMO95 puzzles, Crux Mathematicorum, No. 2, Vol. 22, March 1996, 70.
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