| ADDRESS: | Andreas Schweizer |
| |
Institute of Mathematics, Academia Sinica 6F, Astronomy-Mathematics Building No. 1, Sec. 4, Roosevelt Road Taipei 10617 TAIWAN |
| EMAIL: | myfamilyname@math.sinica.edu.tw |
| where myfamilyname should, of course, be replaced by my family name. | |
| PhD: | Universität des Saarlandes, Saarbrücken, Germany, 1996, Supervisor: Prof. Ernst-Ulrich Gekeler |
| RESEARCH INTERESTS: | Algebraic Number Theory and Arithmetic Geometry, especially: arithmetic of function fields, Drinfeld modules and Drinfeld modular curves, elliptic curves and modular curves, quaternion algebras, non-congruence subgroups |
| 1. |
On the Drinfeld Modular Polynomial $\Phi_T(X,Y)$, J.
Number Theory 52 (1995), 53-68 (free access via journal) |
| 2. |
Modular automorphisms of the Drinfeld modular curves
$X_0({\frak n})$, Collectanea Math. 48 (1997), 209-216 (free access via journal) |
| 3. |
On singular and supersingular invariants of Drinfeld
modules, Ann. Fac. Sci. Toulouse Math. 6 (1997), 319-334 (free access via Numdam) |
| 4. |
Hyperelliptic Drinfeld Modular Curves, in: Drinfeld Modules, Modular Schemes and Applications, (E.-U. Gekeler, M. van der Put, M. Reversat, J. Van Geel, eds.), World Scientific, Singapore, 1997, pp. 330-343 |
| 5. |
Involutory elliptic curves over ${\mathbb F}_q(T)$, J.
Th\'eor. Nombres Bordeaux 10 (1998), 107-123 (free access via Numdam) |
| 6. |
On elliptic curves over function fields of characteristic
two, J. Number Theory 87 (2001), 31-53 (free access via journal) |
| 7. |
On elliptic curves in characteristic 2 with wild additive
reduction, Acta Arith. 91 (1999), 171-180 (free access via Polish Virtual Library of Sciene) |
| 8. |
Extremal elliptic surfaces in characteristic 2 and 3, Manuscripta Math. 102 (2000), 505-521 |
| 9. |
Bielliptic Drinfeld Modular Curves, Asian J. Math. vol. 5, no. 4 (December 2001), 705-720 |
| 10. |
On Drinfeld modular curves with many rational points over
finite fields, Finite Fields Appl. 8 (2002), 434-443 (free access via journal) |
| 11. |
On the uniform boundedness conjecture for Drinfeld modules, Math. Z. 244 (2003), 601-614 |
| 12. |
(with A.W. Mason) The minimum index of a non-congruence subgroup of $SL_2$ over an arithmetic domain, Israel J. Math. 133 (2003), 29-44 |
| 13. |
Torsion of Drinfeld modules and gonality, Forum Math. 16
(2004), 925-941 |
| 14. |
On periodic points under the iteration of additive polynomials, Manuscripta Math. 113 (2004), 25-34 |
| 15. |
(with D. Jeon and C.H. Kim) On the torsion
of elliptic curves over cubic number fields, Acta Arith. 113 (2004),
291-301 |
| 16. |
On the $p^e$-torsion of elliptic curves and elliptic
surfaces in characteristic $p$, Trans. Amer. Math. Soc. 357 (2005),
1047-1059 (free access via journal) |
| 17. |
(with A.W. Mason) The minimum index of a
non-congruence subgroup of $SL_2$ over an arithmetic domain. II: The
rank zero cases, J. London Math. Soc. 71 (2005), 53-68 |
| 18. |
Shared values of meromorphic
functions on compact Riemann surfaces, Arch. Math. (Basel) 84 (2005),
71-78 |
| 19. |
(with A.W. Mason) Non-standard
automorphisms and non-congruence subgroups of $SL_2$ over Dedekind
domains contained in function fields, J. Pure Appl. Algebra 205
(2006), 189-209 (free access via journal) |
| 20. |
(with M. Schütt ) On
Davenport-Stothers inequalities and elliptic surfaces in positive
characteristic, Quarterly J. Math. (Oxford) 59 (2008), 499-522 (article in preprint-arXiv) |
| 21. |
(with A.W. Mason) Nonrational
genus zero function fields and the Bruhat-Tits tree, Communications in Algebra 37 no. 12 (2009), 4241-4258 (article in preprint-arXiv) |
| 22. |
Value-sharing of meromorphic functions on a
Riemann surface, J. Math. Anal. Appl. 365 (2010), 220-228 (article in preprint-arXiv) |
| 23. |
Strong Weil curves over
${\mathbb F}_q(T)$
with small conductor, J. Number Theory 131 (2011), 285-299 (article in preprint-arXiv |
| 24. |
(with M. Schütt ) On the
uniqueness of elliptic K3 surfaces with maximal singular fibre, Ann. Inst. Fourier (Grenoble), to appear (article in preprint-arXiv) |
| 25. |
(with A.W. Mason) The cusp
amplitudes and quasi-level of a congruence subgroup of $SL_2$ over any
Dedekind domain, Proc. London Math. Soc., in press
(article in preprint-arXiv) |
| 26. |
Entire functions sharing simple $a$-points with their first derivative, Houston J. Math., to appear |
| 27. |
(with A.W. Mason) The vertex stabilizers of the Bruhat-Tits tree of a Drinfeld modular group, submitted (article in preprint-arXiv) |
| 28. |
On the uniqueness of $(p,h)$-gonal automorphisms of Riemann surfaces, submitted (article in preprint-arXiv) |
| Survey articles: | |||
| 1. | Some applications of Drinfeld modular curves | pp. 1-6 | Trends in Mathematics, vol. 4, no 2 (December 2001), KAIST, Taejon |