Some remarks on Weierstrass points
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- by James A. Jenkins PDF
- Proc. Amer. Math. Soc. 44 (1974), 121-122 Request permission
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.References
- H. M. Farkas, Weierstrass points and analytic submanifolds of Teichmueller space, Proc. Amer. Math. Soc. 20 (1969), 35–38. MR 232928, DOI 10.1090/S0002-9939-1969-0232928-2 J. V. Uspensky and M. A. Heaslet, Elementary number theory, McGraw-Hill, New York, 1939. MR 1, 38.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 121-122
- MSC: Primary 30A46
- DOI: https://doi.org/10.1090/S0002-9939-1974-0328063-7
- MathSciNet review: 0328063