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On Schoeneberg's theorem

Published online by Cambridge University Press:  18 May 2009

C. Maclachlan
C. Maclachlan
Affiliation:
University of Aberdeen
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Let Sbe a compact Riemann surface of genus g ≥ 2 and σ an automorphism (conformal self-homeomorphism) of S of order n. Let S* = S/ « σ« have genus g*. In [5], Schoeneberg gave a sufficient condition that a fixed point P ∈ S of σ should be a Weierstrass point of S, i.e., that Sshould support a function that has a pole of order less than or equal to g at P and is elsewhere regular.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 202 - 204
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Harvey, W. J., Cyclic groups of automorphisms of a compact Riemann surface, Quart. J. Math. Oxford Ser. (2) 17 (1966), 86–97.Google Scholar
2.Larcher, H., Weierstrass points at the cusps of Γ0(16p) and the hyperellipticity of Γ0(n), Canad. J. Math. 22 (1971), 960–968.CrossRefGoogle Scholar
3.Lewittes, J., Automorphisms of compact Riemann surfaces, Amer. J. Math. 84 (1963), 734–752.Google Scholar
4.Maclachlan, C., Weierstrass points on compact Riemann surfaces, J. London Math. Soc. (2) 3 (1971), 722–724.Google Scholar
5.Schoeneberg, B., Über die Weierstrasspunkte in den Körpern den elliptischen Modulfunktionen, Abh. Math. Sem. Univ. Hamburg 17 (1951), 104–111.CrossRefGoogle Scholar