Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 669-682

ON ASYMMETRIC p-HYPERELLIPTIC RIEMANN SURFACES

Ewa Kozlowska-Walania and Ewa Tyszkowska

Gdansk University, Institute of Mathematics
Wita Stwosza 57, 80-952 Gdansk, Poland; retrakt 'at' mat.ug.edu.pl

Gdansk University, Institute of Mathematics
Wita Stwosza 57, 80-952 Gdansk, Poland; ewa.tyszkowska 'at' mat.ug.edu.pl

Abstract. In this paper we study asymmetric and pseudo-symmetric Riemann surfaces of genus g ≥ 2 with full automorphism group Z_4n for n = 1 or prime. We give necessary and sufficient conditions for the existence of such a surface and we find all values of p and q for which the surface is p-hyperelliptic and (q,n)-gonal.

2010 Mathematics Subject Classification: Primary 30F99; Secondary 14H37.

Key words: Riemann surface, symmetry of Riemann surface, asymmetric Riemann surface, pseudo-symmetric Riemann surface, Fuchsian groups, NEC groups.

Reference to this article: E. Kozlowska-Walania and E. Tyszkowska: On asymmetric p-hyperelliptic Riemann surfaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 669-682.

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doi:10.5186/aasfm.2015.4040