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On triangular (D>n)-actions on cyclic p-gonal Riemann surfaces

Tyszkowska E.

Opuscula Mathematica

2016

Vol. 36, no. 1

103--122

A compact Riemann surface X of genus g > 1 which has a conformal automorphism ρ of prime order p such that the orbit space X/(ρ) is the Riemann sphere is called cyclic p-gonal. Exceptional points in the moduli space Mg of compact Riemann surfaces of genus g are unique surface classes whose full group of conformal automorphisms acts with a triangular signature. We study symmetries of exceptional points in the cyclic p-gonal locus in Mg for which Aut(X)/(ρ is a dihedral group Dn.

Automorphic forms for NEC groups

Alvarez J. P.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 3

291-300

In this paper we extend classical ideas of Poincare on functions associated with Fuchsian Groups (discrete groups of isometries of the hyperbolic metric) to the case where the group contains orientation reversing elements of the hyperbolic plane H.