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A Note on Weierstrass Points

Published online by Cambridge University Press:  20 November 2018

Donald L. McQuillan
Donald L. McQuillan*
Affiliation:
University of Wisconsin, Madison
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In (4) G. Lewittes proved some theorems connecting automorphisms of a compact Riemann surface with the Weierstrass points of the surface, and in (5) he applied these results to elliptic modular functions. We refer the reader to these papers for definitions and details. It is our purpose in this note to point out that these results are of a purely algebraic nature, valid in arbitrary algebraic function fields of one variable over algebraically closed ground fields (with an obvious restriction on the characteristic). We shall also make use of the calculation carried out in (5) to obtain a rather easy extension of a theorem proved in (6, p. 312).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 268 - 272
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Chevalley, C. and Weil, A., Ueber das Verhalten der Integrale erster Gattung bei Automorphismen des Funktionenkörpers, Abh. Math. Sem. Univ. Hamburg, 10 (1934), 358–361.Google Scholar
2. Hecke, E., Ueber ein Fundamental problem aus der Theorie der elliptischen Modulfunktionen, Abh. Math. Sem. Univ. Hamburg, 6 (1928), 235–257.Google Scholar
3. Hecke, E., Ueber das Verhalten der Integrale 1. Gattung bei Abbildungen …, Abh. Math. Sem. Univ. Hamburg, 8 (1930), 271–281.Google Scholar
4. Lewittes, G., Automorphisms of compact Riemann surfaces, Amer. J. Math., 85 (1963), 734–752.Google Scholar
5. Lewittes, G., Gaps at Weierstrass points for the modular group, Bull. Amer. Math. Soc., 69 (1963), 578–582.Google Scholar
6. McQuillan, D. L., A generalization of a theorem of Hecke, Amer. J. Math., 84 (1962), 306–316.Google Scholar
7. Reiner, I. and Curtis, C., Representation theory of finite groups and associative algebras (New York, 1962).Google Scholar
8. Schoeneberg, B., Ueber die Weier strass Punkte in den Körpern der Elliptischen Modulfunktionen, Abh. Math. Sem. Univ. Hamburg, 17 (1951), 104–111.Google Scholar