Homepage of  Andreas Schweizer


ADDRESS:



Andreas Schweizer





Department of Mathematics
Korea Advanced Institute of Science and Technology (KAIST)
Daejeon 305-701
SOUTH KOREA

EMAIL:





myfamilyname@kaist.ac.kr





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.
Also: value-sharing of meromorphic functions.


Since January 2016 I am one of the editors of the journal Archiv der Mathematik.


PUBLICATIONS:

Research papers in (chrono)logical order:

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, 
Arch. Math. (Basel) 98 (2012), 591-598
(article in preprint-arXiv)





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


FR 6.1 Mathematik | Arbeitsgruppe

Last changes:  May 17, 2016