My research interests include algebraic number theory, algebraic curves, abelian varieties, special values of modular functions, cryptography, divisibility sequences, and computational number theory.

See also the work of my students.

In preparation
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Elliptic nets and modular units
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Rational CM points in the moduli space of curves of genus three
with Pınar Kılıçer
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Elliptic divisibility sequences over function fields
with Bartosz Naskrȩcki
-and more
Articles and preprints
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Generators of the group of modular units for Γ1(N) over Q
accepted for publication in Annales Henri Lebesgue (2022)
journal
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The CM class number one problem for curves of genus 2
with Pınar Kılıçer
Research in Number Theory, Vol. 9 (2023), number 15
journal
arXiv
code
thesis
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Generalized class polynomials
with Marc Houben
Research in Number Theory, Vol. 8 (2022), number 103, pp 1 - 26
journal
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Primitive divisors of elliptic divisibility sequences over function fields with constant j-invariant
with Bartosz Naskrȩcki
Journal of Number Theory, Vol. 213 (2020), pp 152 - 186
journal
arXiv
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Primes dividing invariants of CM Picard curves
with Pınar Kılıçer, Elisa Lorenzo García
Canadian Journal of Mathematics, Vol. 72 (2020), number 2, pp 480 - 504
journal
arXiv
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A bound on the primes of bad reduction for CM curves of genus 3
with Pınar Kılıçer, Kristin Lauter, Elisa Lorenzo García, Rachel Newton, Ekin Ozman
Proc. Amer. Math. Soc., Vol. 148 (2020), pp 2843 - 2861
journal
arXiv
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Plane quartics over Q with complex multiplication
with Pınar Kılıçer, Hugo Labrande, Raynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling
Acta Arithmetica, Volume 185 (2018), number 2, pp 127 - 156
journal
arXiv
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On polarised class groups of orders in quartic CM fields
with Gaetan Bisson
Math. Res. Lett., Vol. 24 (2017), number 2, pp 247 - 270
arXiv
journal
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Schertz style class invariants in dimension 2
with Andreas Enge
preprint, 2016
arXiv
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Examples of CM curves of genus two defined over the reflex field
with Florian Bouyer
LMS Journal of Computation and Mathematics, Vol. 18 (2015), issue 01, pp 507-538
arXiv
journal
code and data
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Curves in characteristic 2 with non-trivial 2-torsion
with Wouter Castryck and Damiano Testa
Advances in Mathematics of Communications (AMC), Vol. 8 (2014), no. 4, pp 479--495
arXiv
journal
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Computing Igusa Class Polynomials
Mathematics of Computation, Vol. 83 (2014), pp 275--309
arXiv
journal
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Abelian surfaces admitting an (l,l)-endomorphism
with Reinier Bröker and Kristin Lauter
Journal of Algebra, Vol. 394 (2013), pp 374--396
arXiv
journal
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An explicit version of Shimura's reciprocity law for Siegel modular functions
preprint, 2012
arXiv
Sage code
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Algebraic divisibility sequences over function fields
with Patrick Ingram, Valéry Mahé, Joseph H. Silverman, Katherine E. Stange
J. Aust. Math. Soc. 92 (2012), 99-126
journal
arXiv
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A CM construction for curves of genus 2 with p-rank 1
with Laura Hitt, Gary McGuire, Michael Naehrig
Journal of Number Theory, Vol. 131 (2011), No. 5, pp. 920-935
journal
arXiv
errata
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Divisibility sequences for elliptic curves with complex multiplication
Algebra & Number Theory, Vol. 2 (2008), No. 2, pp. 183-208
journal
pdf (old)
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Abelian varieties with prescribed embedding degree
with David Freeman and Peter Stevenhagen
ANTS-VIII Banff 2008, Springer Lecture Notes in Computer Science 5011
journal
arXiv
Thesis
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Complex multiplication of abelian surfaces
PhD thesis, Universiteit Leiden (2010)
link / pdf
errata / cover
stellingen