Geodesic
An Elementary Proof of a Fixed Point Theorem of J. Lewittes and D. L. McQuillan
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 99-101

Voir la notice de l'article provenant de la source Cambridge University Press

In (3), J. Lewittes establishes a connection between the number of fixed points of an automorphism of a compact Riemann surface and Weierstrass points on the surface; Lewittes′ techniques are analytic in nature. In (4), D. L. McQuillan proved the result by purely algebraic methods and extended it to arbitrary algebraic function fields in one variable over algebraically closed ground fields, but with restriction to tamely ramified places. In this paper we will give a different proof of the theorem and show that it is an elementary consequence of the Riemann-Hurwitz relative genus formula. Moreover, we can remove the tame ramification restriction. 
Wayman, Arthur K. An Elementary Proof of a Fixed Point Theorem of J. Lewittes and D. L. McQuillan. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 99-101. doi: 10.4153/CMB-1978-015-8
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[1] 1. Boseck, H., “Zur Théorie der Weierstrasspunkte,” Math. Nachr. 19 (1958), 29-63. Google Scholar

[2] 2. Chevalley, C., Introduction to the Theory of Algebraic Functions of One Variable, Amer. Math. Soc, New York, 1951. Google Scholar

[3] 3. Lewittes, J., “Automorphisms of compact Riemann surfaces,” Amer. J. Math., 85 (1963), 734-752. Google Scholar

[4] 4. McQuillan, D. L., “A note on Weierstrass points,” Canad. J. Math., 19 (1967), 268-272. Google Scholar

[5] 5. Schmidt, F. K., “Zur arithmetischen Theorie der algebraischen Funktionen. II. Allgemeine Théorie der Weierstrasspunkte” Math. Zeit. 45 (1939), 75-96. Google Scholar

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