How many quasiplatonic surfaces?

We show that the number of isomorphism classes of quasiplatonic Riemann surfaces of genus <= g has o growth of typ g exp (log g). The number of non-isomorphic regular dessins of genus <= g has the same growth type

ABC for polynomials, dessins d'enfants, and uniformization : a survey

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

Betriebsindividuelle Entwicklung von Natur und Landschaft vor dem Hintergrund der Förderkulisse - Ein Diskussionsbeitrag

The present, for all parties unsatisfying governmental grant system of agricultural nature protection should be adapted in the future individual farm approaches. Methods referring to this are already developed. Instead of invariable directions given all over the country, the applicants formulate actions exactly adjusted for the special locality and the individual farm. An accredited expert attests the conformity of the plan with the laws of nature protection. Consultation is a further topic for governmental granting. All granted actions are to be made transparent to the public. This enhances private-official networks as required by the European Agricultural Convention

Semi-Arithmetic Fuchsian Groups and Modular Embeddings

Arithmetic Fuchsian groups are the most interesting and most important Fuchsian groups owing to their significance for number theory and owing to their geometric properties. However, for a fixed signature there exist only finitely many non-conjugate arithmetic Fuchsian groups; it is therefore desirable to extend this class of Fuchsian groups. This is the motivation of our definition of semi-arithmetic Fuchsian groups. Such a group may be defined as follows (for the precise formulation see Section 2). Let Γ be a cofinite Fuchsian group and let Γ2 be the subgroup generated by the squares of the elements of Γ. Then Γ is semi-arithmetic if Γ is contained in an arithmetic group Δ acting on a product Hr of upper halfplanes. Equivalently, Γ is semi-arithmetic if all traces of elements of Γ2 are algebraic integers of a totally real field. Well-known examples of semi-arithmetic Fuchsian groups are the triangle groups (and their subgroups of finite index) which are almost all non-arithmetic with the exception of 85 triangle groups listed by Takeuchi [16]. While it is still an open question as to what extent the non-arithmetic Fuchsian triangle groups share the geometric properties of arithmetic groups, it is a fact that their automorphic forms share certain arithmetic properties with modular forms for arithmetic groups. This has been clarified by Cohen and Wolfart [5] who proved that every Fuchsian triangle group Γ admits a modular embedding, meaning that there exists an arithmetic group Δ acting on Hr, a natural group inclusion f:Γ→Δ and a compatible holomorphic embedding F:H→Hr that is with F(yZ)=f(y)F(z) for all γ∈Γ and all z∈

Überörtliche Biotopverbundplanungen : eine planerische Grundlage für den Straßenbau

Anhand von drei OU im Zuge von Bundesstraßen wird dargestellt, wie die überörtliche Biotopverbundplanung dazu beitragen kann, Eingriffe nicht nur punktuell-lokal, sondern im größeren Zusammenhang der Biotopverbundsysteme zu bewerten und zu bewältigen. Die Biotopverbundplanung stellt einen Ideen- und Flächenpool bereit, Maßnahmen aus nicht ausgleichbaren Eingriffen sinnvoll zu konzentrieren und mit bestmöglicher Wirkung für Natur und Landschaft umzusetzen. Die Straßenbauverwaltung greift die Vorschläge der Biotopverbundplanung gern auf, wie weitere, bereits realisierte Vorhaben zeigen. Allerdings darf man nicht übersehen, dass Kompensationsmaßnahmen für Eingriffe an anderer Stelle bestenfalls dazu beitragen, die Qualität der Biotopverbundsysteme auf dem gegenwärtigen Stand zu erhalten

Algebraic values of Schwarz triangle functions

We consider Schwarz maps for triangles whose angles are rather general rational multiples of pi. Under which conditions can they have algebraic values at algebraic arguments? The answer is based mainly on considerations of complex multiplication of certain Prym varieties in Jacobians of hypergeometric curves. The paper can serve as an introduction to transcendence techniques for hypergeometric functions, but contains also new results and examples