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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

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5.Schoeneberg, B., Über die Weierstrasspunkte in den Körpern den elliptischen Modulfunktionen, Abh. Math. Sem. Univ. Hamburg 17 (1951), 104–111.CrossRefGoogle Scholar