Note that the preprints on this page might differ from the published versions.
(with Jürgen Klüners) Enumerating orders in number fields arXiv
(with Jürgen Klüners) Chow groups of one-dimensional noetherian domains, Research in Number Theory 10 (2024) no. 89. DOI LinkarXiv
Appendix to Klaus Hulek and Michael Lönne, Moduli of elliptic K3 surfaces: monodromy and Shimada root lattice strata, Algebraic Geometry 9 (2022) no. 2, 159--213. DOI LinkarXiv
(with Fabien Narbonne, Christophe Ritzenthaler and Damien Robert) Spanning the isogeny class of a power of an elliptic curve, Mathematics of Computation 91 (2022), 401--449. DOI LinkarXiv
(with Gabriele Nebe) Binary hermitian lattices over number fields, Exp. Math. 31 (2022) no. 1, 280--301. DOI Linkpreprint
Determinant groups of hermitian lattices over local fields, Archiv der Mathematik, 113 (2019), no. 4, 337--347. DOI Linkpreprint
Automorphisms of even unimodular lattices over number fields, Journal of Number Theory, 197 (2019), 121--134. DOI Linkpreprint
(with Gabriele Nebe) Quaternary quadratic lattices over number fields, International Journal of Number Theory, 15 (2019), 309--325. DOI Linkpreprint
One class genera of exceptional groups over number fields, J. Théorie Nombres Bordeaux, 30 (2018), no. 3, 847--857. DOI Linkpreprint
(with Gabriele Nebe) One class genera of lattice chains over number fields. In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, eds. G. Böckle, W. Decker and G. Malle, Springer, 2018, 503--532. DOI Linkpreprint
(with Marion Rüther) The constructive membership problem for discrete two-generator subgroups of SL(2,R), J. Algebra 480 (2017), 519--548. DOI Linkpreprint
(with David Lorch) Ternary quadratic forms over number fields with small class number, Journal of Number Theory 161 (2016), 343--361. DOI Linkpreprint A list of all quaternion orders of type or class number at most two is available here.
One-class genera of maximal integral quadratic forms. Journal of Number Theory 136C (2014), 375--393. DOI Linkpreprint A list of these genera is available here.
(with Bettina Eick and Charles R. Leedham-Green) The constructive membership problem for discrete free subgroups of rank 2 of SL(2,R), LMS J. Comput. Math. 17 (2014), no. 1, 345--359. DOI LinkpreprintMagma code
(with Charles R. Leedham-Green) Computing with subgroups of the modular group, Glasgow Mathematical Journal 57 (2014), no. 1, 173--180. DOI LinkpreprintMagma code
(with David Lorch) Single-class genera of positive integral lattices, LMS J. Comput. Math. 16 (2013), 172--186. DOI Link
(with Michael H. Mertens) On an Analogue to the Lucas-Lehmer-Riesel test using Elliptic Curves, INTEGERS 13 (2013), A15. Link
A normal form for definite quadratic forms over F_q[t]. Math. Comp. 81 (2012), 1619--1634. DOI Linkpreprint
Finite symplectic matrix groups. Exp. Math. 20 (2011) no. 2, 217--228. DOI Link
(with John Voight) Algorithmic enumeration of ideal classes for quaternion orders. SIAM J. Comput. (SICOMP) 39 (2010), no. 5, 1714--1747. DOI Linkcorrected
Theses
Definite quadratic and hermitian forms with small class number. Habilitationsschrift. RWTH Aachen University, 2016 pdf The lattices of class number one and two are available here
Finite symplectic matrix groups. Dissertation. RWTH Aachen University, 2009 pdf The invariant forms given in the appendix are available here.
Konstruktive Idealtheorie in Quaternionenalgebren. Diplomarbeit. Universität Ulm, 2005 pdf
Magma Code
Most of the algorithms of my papers are shipped with Magma. Below are some packages that have not been included in Magma (yet).
