Geodesic
On Schoeneberg's theorem
Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 202-204

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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. 
Maclachlan, C. On Schoeneberg's theorem. Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 202-204. doi: 10.1017/S001708950000197X
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[2] 2.Larcher, H., Weierstrass points at the cusps of Γ(16p) and the hyperellipticity of Γ(n), Canad. J. Math. 22 (1971), 960–968. Google Scholar | DOI

[3] 3.Lewittes, J., Automorphisms of compact Riemann surfaces, Amer. J. Math. 84 (1963), 734–752. Google Scholar

[4] 4.Maclachlan, C., Weierstrass points on compact Riemann surfaces, J. London Math. Soc. (2) 3 (1971), 722–724. Google Scholar

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

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