Department of Mathematics and Statistics
Publications
- Perfect unary forms over real quadratic fields, J. Théor. Nombres Bordeaux (2013), 1–17, accepted.
- with Paul Gunnells, Modular forms and elliptic curves over the cubic field of discriminant −23, Int. J. Number Theory 9 (2013), no. 1, 53-76.
- Computing modular forms for ${\rm GL}_2$ over certain number fields, Computations with Modular Forms 2011 Proceedings, 2013.
- with Farshid Hajir and Paul Gunnells, Modular forms and elliptic
curves over the field of fifth roots of unity, Exp. Math. 22 (2013), no. 2, 203-216.
- Computing modular forms using Voronoi polyhedra (extended abstract), Mathematisches Forschungsinstitut Oberwolfach, Report No. 35/2011, Explicit Methods in Number Theory
- On modular forms and elliptic curves over $\mathbb{Q}(\zeta_5)$, RIMS Automorphic
forms, trace formulas, and zeta functions (2011), Proceedings.
- with Adriano Bruno, The arithmetic of planar binary trees, Involve 4-1 (2011), 1-11.
- Hyperbolic tessellations associated to Bianchi groups, 6197 (2010),
385 - 396, 9th International Symposium, Nancy, France, ANTS-IX, July
19-23, 2010, Proceedings.
- Binary Hermitian forms over a cyclotomic field, J. Algebra 322
(2009), 4132-4142.
- Computing Hecke operators on Bianchi forms, Tech. Report, Magma computational group: University of Sydney, 2009.
- Modular forms over imaginary quadratic fields, package available in
Magma V2.16, 2009.
- with Paul Gunnells, Hecke operators and Hilbert modular forms,
Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 5011,
Springer, Berlin, 2008, pp. 387-401.
- Integral cohomology of certain Picard modular surfaces, preprint.
- Elliptic points of the Picard modular group, Monatsh. Math. (2009), no. 156, 391-396.
- An explicit spine for the Picard modular group over the Gaussian integers, J. Number Theory 128 (2008), no. 1, 207-234.
- On the existence of spines for $\mathbb{Q}$-rank 1 groups, Selecta Math. (N.S.)
12 (2006), no.3-4, 541-564.
- On the existence of spines for $\mathbb{Q}$-rank 1 groups, Ph.D. Thesis, Duke
University, 2005.
