## Higher Weierstrass points on $X_{0}(p)$

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- by Scott Ahlgren and Matthew Papanikolas
- Trans. Amer. Math. Soc.
**355**(2003), 1521-1535 - DOI: https://doi.org/10.1090/S0002-9947-02-03204-X
- Published electronically: November 20, 2002
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## Abstract:

We study the arithmetic properties of higher Weierstrass points on modular curves $X_{0}(p)$ for primes $p$. In particular, for $r\in \{2, 3, 4, 5\}$, we obtain a relationship between the reductions modulo $p$ of the collection of $r$-Weierstrass points on $X_{0}(p)$ and the supersingular locus in characteristic $p$.## References

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## Bibliographic Information

**Scott Ahlgren**- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- Email: ahlgren@math.uiuc.edu
**Matthew Papanikolas**- Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
- Email: map@math.brown.edu
- Received by editor(s): July 31, 2002
- Received by editor(s) in revised form: September 19, 2002
- Published electronically: November 20, 2002
- Additional Notes: The first author thanks the National Science Foundation for its support through grant DMS 01-34577
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**355**(2003), 1521-1535 - MSC (2000): Primary 11G18; Secondary 11F33, 14H55
- DOI: https://doi.org/10.1090/S0002-9947-02-03204-X
- MathSciNet review: 1946403