Research

I work in Number Theory. More specifically, my main interst lies in Arithmetic Geometry, where I work on Elliptic curves, Drinfeld modules, Drinfeld modular forms and related topics. Other interests include Ducci sequences and orders of elements in finte fields.

Publications

Note: for copyright reasons, some of the following PDF files are not the final, published versions. Also, this is page is under contruction, so most links are still broken.
  1. Drinfeld modular forms of arbitrary rank (With Dirk Basson and Richard Pink). Monograph. This text updates (e.g. Prop 5.16) and combines the three preprints:
  2. Multiplicative orders of Gauss periods and the arithmetic of real quadratic fields. Finite Fields Appl., 73 (2021). [PDF] arXiv:2006.10344

  3. Generic monodromy of Drinfeld modular varieties in special characteristic. (With Gebhard Böckle) In: ``Abelian Varieties and Number Theory'' (M. Jarden, T. Shaska, eds.) Contemp. Math., Amer. Math. Soc. 767, (2021), 147--160. [PDF] arXiv:1912.09820

  4. Heights and isogenies of Drinfeld modules. (With Fabien Pazuki and Heriniaina Razafinjatovo) Acta Arith. 197 no.2 (2021), 111-128. arXiv:1908.03485 [PDF]

  5. Lower bounds for periods of Ducci sequences. (With Igor Shparlinski) Bull. Aust. Math. Soc. 102 no.1 (2020), 31-38. arXiv:1909.04462

  6. Periods of Ducci sequences and odd solutions to a Pellian equation. Bull. Aust. Math. Soc. 100 no.2 (2019), 201-205.

  7. On certain Drinfeld modular forms of higher rank. (with Dirk Basson). J. Théor. Nombres Bordeaux 29 no.3 (2017), 827-843. [PDF]

  8. A note on Gekeler's h-function. Arch. Math. 107 (2016), 305-313. [PDF] The final publication is available at Springer via http://dx.doi.org/doi:10.1007/s00013-016-0923-1. arXiv:1605.02567

  9. Drinfeld modular polynomials in higher rank II: Kronecker congruences. (With Hans-Georg Rück). J. Number Theory 165 (2016), 1-14. [PDF] arXiv:1303.4086

  10. Explicit Drinfeld moduli schemes and Abhyankar's generalized iteration conjecture. J. Number Theory 160 (2016), 432-450. [PDF] arXiv:1503.06420

  11. Newton identities for Weierstrass products. Amer. Math. Monthly 119, no. 9 (2012), 796-799. [PDF]

  12. Special subvarieties of Drinfeld modular varieties. J. reine angew. Math. 668 (2012), 35-57. [PDF] arXiv:math/0503452

  13. Ducci sequences and cyclotomic fields. J. Difference Equ. Appl. 16 (2010), no. 7, 847-862. [PDF]

  14. Torsion bounds for elliptic curves and Drinfeld modules. J. Number Theory 130 (2010), 1241-1250. [PDF]

  15. Drinfeld modular polynomials in higher rank. J. Number Theory 129 (2009), 59-83. (With Hans-Georg Rück) [PDF] arXiv:math/0701291

  16. Heegner points and the rank of elliptic curves over large extensions of global fields. Canadian J. Math. 60 (2008), no.3, 481-490. (With Bo-Hae Im) [PDF] arXiv:math/0604107

  17. The André-Oort conjecture for Drinfeld modular varieties. C. R. Math. Acad. Sci. Paris, Ser. I, 344 (2007), 733-736. [PDF]

  18. Ducci sequences in higher dimensions. Integers: Electronic Journal of Combinatorial Number Theory 7 (2007), #A24. [PDF]

  19. Ducci sequences and cyclotomic polynomials. Finite Fields Appl. 13 (2007), 293-304. (With Ernest Lötter and Brink van der Merwe.) [PDF]

  20. CM points on products of Drinfeld modular curves. Trans. Amer. Math. Soc. 359 (2007), 1351-1374. [PDF] arXiv:math/0407334

  21. Monodromy groups associated to non-isotrivial Drinfeld modules in generic characteristic. In: "Number Fields and Function Fields - Two Parallel Worlds", (G. van der Geer, B. Moonen, R. Schoof, eds.), Progress in Mathematics, 239, p61-69, Birkhäuser Verlag, 2005. (With Richard Pink.) [PDF] arXiv:math/0407335

  22. The André-Oort conjecture for products of Drinfeld modular curves. J. reine angew. Math. 579 (2005), 115-144. [PDF] arXiv:math/0303038

  23. Images of isogeny classes on modular elliptic curves. Math. Res. Lett. 11 (2004), 649-651. [PDF] arXiv:math/0407336

  24. Higher Heegner points on elliptic curves over function fields. J. Number Theory 104 (2004), 315-326. [PDF] arXiv:math/0304216

  25. La conjecture d'André-Oort pour le produit de deux coubres modulaires de Drinfeld. C. R. Math. Acad. Sci. Paris 335 (2002), no. 11, 867--870. [PDF]

  26. Distinguished liftings and the André-Oort conjecture. Quaest. Math. 25(3) (2002), 363-380. [PDF]

  27. Heights of CM points on complex affine curves. Ramanujan J. 5 (2001), 311-317. [PDF]

  28. Ducci sequences over abelian groups. Comm. Algebra 27.12 (1999), 5999-6013. [PDF]

  29. A note on a paper by Glaser and Schöffl. Fibonacci Quart. 36.5 (1998), 463-466. [PDF]

  30. Strategy and complexity of the game of squares. Bull. London. Math. Soc 30 (1998), 274-282. (With Mike Robson) [PDF]

  31. Line profile variations in the spectra of the gamma Dor star HR 2740, In: IAU Symposium 185 "New Eyes to See Inside the Sun and Stars", (F.-L. Deubner, J. Christensen-Dalsgaard, D. Kurtz, eds) Kyoto, Japan, 18-22 August, 1997, p. 387. (5th author, with E. Poretti, L. Mantegazza, C. Koen, P. Martinez, D. De Alwis and H. Haupt). [PDF]

  32. Discovery and analysis of gamma doradus type pulsations in the F0 IV star HR 2740 QW pup, Mon. Not. R. Astron. Soc. 292 (1997), 621-630. (4th author, with E. Poretti, C. Koen, P. Martinez, D. de Alwis and H. Haupt) [PDF]