Within the framework of this thesis, three studies are presented that investigated cultural similarities and differences of preschool aged children’s self- and family-drawings. The research was guided by the assumption that besides the basic structure of the drawing, specific drawing characteristics would vary cross-culturally, according to differences in cultural models and the associated understanding of self and others. Based on an ecocultural approach, families were systematically selected from diverse cultural contexts across and within national boundaries, representing three different cultural models: (1) the cultural model of psychological autonomy (characteristic for Western urban middle-class contexts), (2) the cultural model of hierarchical relatedness (representative for non-Western rural traditional contexts), and (3) mixed cultural models of autonomous relatedness (e.g., non-Western urban middle-class contexts, migration contexts). The participating children were of similar age, gender distribution, and had reached comparable structural levels of human figure drawings. Overall, the studies revealed three main findings. First, it could be confirmed that there are basic similarities in children’s graphic development. In line with previous reports, the studies demonstrated that the structural composition of the human figure as well as production principles did not differ significantly across cultures. Second, several content-based drawing features varied with cultural context and the associated cultural model. In particular, figure size, the facial depiction, and gender-specific characteristics could be linked to the culturally shaped understanding of self and others in the respective cultural context. Third, it was shown that the composition of children’s family-drawings corresponded to the structure of families in the particular cultural context, mainly with regard to number and position of family members, figure size- and gender-differentiation. The results are discussed with a focus on the role of general and culture-specific drawing characteristics in preschool aged children’s drawings of self and family. Based on these and former research findings, an integrative framework of children’s self- and family-drawings is proposed in order to shed light on the origin and relationship of the investigated drawing characteristics. Open research questions are pointed out, as well as limitations and practical implications of the study results.

Diese Dissertation behandelt nicht-holomorphe Diese Dissertation behandelt nicht-holomorphe Eisensteinreihen und Dessins d''Enfants. Nicht-holomorphe Eisensteinreihen entstehen aus Untergruppen der Modulgruppe, indem man über alle Elemente der Gruppe modulo dem Stabilisator einer Spitze aufsummiert. Die zweite Struktur, Dessins d''Enfants, sind bipartite Graphen die in topologische Flächen eingebettet sind. Dessins d''Enfants stehen in Korrespondenz zu Belyi-Paaren und Untergruppen der Modulgruppe von endlichem Index. Deshalb bestehen zwischen Eisensteinreihen und Dessins d''Enfants Verbindungen und ein Schwerpunkt dieser Arbeit ist es, Informationen und Wissen über das eine Objekt in das andere zu übertragen. Bezüglich Dessins d''Enfants beschäftigen wir uns mit Symmetrien. Wir waren in der Lage, Automorphismen von algebraischen Kurven im assoziierten Dessin, in der zugehörigen Untergruppe sowie insbesondere auf den Spitzen zu interpretieren. Außerdem beschreiben wir die Zusammenhänge zwischen Dessins für Untergruppen, dadurch können wir für zwei Untergruppen anhand ihres Dessins entscheiden, ob sie in einander enthalten sind. In Kombination mit hier erbrachten Resultaten zu den Hauptkongruenzuntergruppen führt dies zu einem implementierten Algorithmus, der prüft, ob eine Gruppe eine Kongruenzuntergruppe ist oder nicht. Auf der Seite der Eisensteinreihen untersucht dieser Text Streukonstanten, Greensche Funktionen und Kroneckergrenzformeln. In der Streumatrix fanden wir Symmetrien (für bestimmte Gruppen). Für Greensche Funktionen wurde eine Spurformel bewiesen. Wir zeigten, dass Eisensteinreihen eine Identität erfüllen, die wir Kroneckergrenzformel nennen; sie vergleicht den konstanten Term der Eisensteinreihe mit Funktionen, die von ausgezeichneten Modulformen kommen. Die Dissertation gipfelt in der Berechnung der Streukonstanten für die Untergruppen assoziiert zu den Fermatkurven, die fast alle Nichtkongruenzuntergruppen sind. / In this dissertation non-holomorphic Eisenstein series and Dessins d''Enfants are considered. Non-holomorphic Eisenstein series are created out of subgroups of the modular 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 embedded into topological surfaces. There is a correspondence between Dessins D''Enfants, Belyi pairs and subgroups of the modular group of finite index. Therefore Eisenstein series and Dessins d''Enfants are related and a focus of this work is how to use the one to find information about the other. The main results concerning Dessins d''Enfants in this thesis are investigations of symmetries of Dessins. We have been able to interpret automorphisms of algebraic curves on the associated Dessin, the subgroups and in particular the set of cusps. Furthermore, we describe the relation of Dessins for subgroups. Therefore, with help of the Dessins we can decide if two subgroups are contained in each other. Together with our results on the Dessins for principal congruence subgroups this leads to an implemented algorithm that checks if a subgroup is a congruence subgroup or not. On the side of Eisenstein series we consider scattering constants, Green''s functions and Kronecker limit formulas. We found symmetries in the scattering matrix for certain groups. For Green''s functions we established a trace formula. We showed that Eisenstein series fulfill an identity we call Kronecker limit formula in which they are compared with functions coming from certain modular forms. Most of the work done in this thesis culminates in the calculation of the scattering constants for the subgroups associated to Fermat curves; most of these groups are non-congruence.