Belyi pairs and scattering constants [Elektronische Ressource] / von Anna Elisabeth Posingies

Belyi pairs and scattering constantsDISSERTATIONzur Erlangung des akademischen GradesDr. rer. nat.im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät IIHumboldt-Universität zu BerlinvonDipl.-Math. Anna Elisabeth Posingies8. September 1980, BerlinPräsident der Humboldt-Universität zu Berlin:Prof. Dr. Dr. h.c. Christoph MarkschiesDekan der Mathematisch-Naturwissenschaftlichen Fakultät II:Prof. Dr. Peter FrenschGutachter:(i) Prof. Dr. Jürg Kramer(ii) Prof. Dr. Ulf Kühn(iii)Prof. Dr. Jürgen Wolfarteingereicht am: 25. Mai 2010Tag der mündlichen Prüfung: 14. September 2010AbstractIn this dissertation non-holomorphic Eisenstein series and Dessins d’Enfants areconsidered. Non holomorphic Eisenstein series are created out of subgroups of themodular group by summing up over all elements modulo the stabilizer of a cusp.The second main object, Dessins d’Enfants, are bipartite graphs that are embeddedinto topological surfaces.There is a correspondence between Dessins D’Enfants, Belyi pairs (a non-singular1algebraiccurvewithamaptoP ramifiedaboveatmostthreepoints)andsubgroupsΓ ⊂ Γ(2) of finite index. Therefore Eisenstein series and Dessins d’Enfants arerelated and a focus of this work is how to use the one to find information about theother.The main results concerning Dessins d’Enfants in this thesis are investigations ofsymmetries of Dessins.