An example of an arithmetic Fuchsian group.
In these notes we construct explicit examples of degenerations on the noded Schottky space of genus g ≥ 3. The particularity of these degenerations is the invariance under the action of a dihedral group of order 2g. More precisely, we find a two-dimensional complex manifold in the Schottky space such that all groups (including the limit ones in the noded Schottky space) admit a fixed topological action of a dihedral group of order 2g as conformal automorphisms.
Let be an end of a Riemann surface with null boundary and let be a lacunary end with a closed set . We study minimal functions in and to show that and have similar properties if is thinly distributed on the ideal boundary. We discuss the behaviour of analytic functions in and relation between the existence of analytic functions of some classes in and the structure of Martin’s boundary points over the end . Also we show that the existence of complicated Martin’s boundary points...
The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.