ADDRESS: | Andreas Schweizer | ||||
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Department of Mathematics Korea Advanced Institute of Science and Technology (KAIST) Daejeon 305-701 SOUTH KOREA |
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EMAIL: |
myfamilyname@kaist.ac.kr |
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where myfamilyname should, of course, be replaced by my family name. | |||||
PhD: |
Universität des Saarlandes, Saarbrücken, Germany, 1996, Supervisor: Prof. Ernst-Ulrich Gekeler |
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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. Also: value-sharing of meromorphic functions. |
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 Science) |
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 (free access via journal) |
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 Daeyeol Jeon and Chang Heon Kim) On the torsion
of elliptic curves over cubic number fields, Acta Arith. 113 (2004), 291-301 (free acces via journal) |
16. |
On the $p^e$-torsion of elliptic curves and elliptic
surfaces in characteristic $p$, Trans. Amer. Math. Soc. 357 no. 3 (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 Matthias 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) (free access via journal) |
23. |
Strong Weil curves over
${\mathbb F}_q(T)$
with small conductor, J. Number Theory 131 (2011), 285-299 (article in preprint-arXiv) (free access via journal) |
24. |
(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. 105 (2012), 311-341 (article in preprint-arXiv) |
25. |
On the uniqueness of $(p,h)$-gonal automorphisms of Riemann surfaces, |
26. |
(with Matthias Schütt) On the uniqueness of elliptic K3 surfaces with maximal singular fibre, Ann. Inst. Fourier (Grenoble) 63 no. 2 (2013), 689-713 (article in preprint-arXiv) |
27. |
Entire functions sharing simple $a$-points with their first derivative, Houston J. Math. 39 no. 4 (2013), 1137-1148 (article in preprint-arXiv) (journal-version) Please note that the address and email given in the journal article are out of date. |
28. |
(with
A.W. Mason) The stabilizers in a Drinfeld modular group of the vertices
of its Bruhat-Tits tree: an elementary approach, Internat. J. Algebra Comput. 23 no. 7 (2013), 1653-1683 (article in preprint-arXiv) |
29. |
(with Hsiu-Lien Huang and Julie Tzu-Yueh Wang) On the exponential local-global principle for meromorphic functions and algebraic functions, Arch. Math. (Basel) 102 (2014), 423-436 (article in preprint-arXiv) |
30. |
(with
A.W. Mason) Elliptic points of the Drinfeld modular groups,
Math. Z. 279 issue 3-4 (2015), 1007-1028 (article in preprint-arXiv) |
31. |
(with A.W. Mason) Genuine non-congruence subgroups of Drinfeld modular groups, J. Pure Appl. Algebra 220 issue 10 (2016), 3345-3362 (article in preprint-arXiv) |
32. |
Entire functions sharing simple a-points with their first derivative II, preprint (article in preprint-arXiv) |
33. |
Some remarks on bielliptic and trigonal curves, preprint (article in preprint-arXiv) |
34. |
On the exponent of the automorphism group of a compact Riemann surface, preprint, (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 |