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An example of degeneration on the noded Schottky space.

Rubén A. Hidalgo (1998)

Revista Matemática Complutense

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.

Analytic functions in a lacunary end of a Riemann surface

Zenjiro Kuramochi (1975)

Annales de l'institut Fourier

Let G be an end of a Riemann surface with null boundary and let G ' be a lacunary end with a closed set F = G - G ' . We study minimal functions in G and G ' to show that G and G ' have similar properties if F is thinly distributed on the ideal boundary. We discuss the behaviour of analytic functions in G ' and relation between the existence of analytic functions of some classes in G ' and the structure of Martin’s boundary points over the end G . Also we show that the existence of complicated Martin’s boundary points...

Another algebraic proof of Weil's reciprocity

Emma Previato (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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.

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