TY  - CONF
A1  - Wolfart, Jürgen
T1  - ABC for polynomials, dessins d'enfants, and uniformization : a survey
T2  - Elementare und analytische Zahlentheorie : (Tagungsband) ; proceedings ELAZ-conference May 24-28, 2004
N2  - The main subject of this survey are Belyi functions and dessins d'enfants on Riemann surfaces. Dessins are certain bipartite graphs on 2-mainfolds defining there are conformal and even an algebraic structure. In principle, all deeper properties of the resulting Riemann surfaces or algebraic curves should be encoded in these dessins, but the decoding turns out to be difficult and leads to many open problems. We emphasize arithmetical aspects like Galois actions, the relation to the ABC theorem in function filds and arithemtic questions in uniformization theory of algebraic curves defined over number fields.
Y1  - 2005
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4316
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30-11728
UR  - http://www.math.uni-frankfurt.de/~wolfart/wolfart.html
SN  - 3-515-08757-5
SP  - 313
EP  - 345
PB  - Steiner
CY  - Stuttgart
ER  -