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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some remarks on Weierstrass points


Author: James A. Jenkins
Journal: Proc. Amer. Math. Soc. 44 (1974), 121-122
MSC: Primary 30A46
MathSciNet review: 0328063
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Abstract: The author proves that, at a point $ P$ on a closed Riemann surface of genus $ g$, if $ h$ is the first nongap at $ P$ and $ k$ is relatively prime to $ h$, then $ k$ is a gap if $ g > \tfrac{1}{2}(h - 1)(k - 1)$. A consequence is that at the Weierstrass points of a closed Riemann surface, if the first nongap is a prime, the situation mirrors that in the hyperelliptic case, at least in a limiting sense.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0328063-7
PII: S 0002-9939(1974)0328063-7
Article copyright: © Copyright 1974 American Mathematical Society