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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Scott Ahlgren and Matthew Papanikolas
Journal: Trans. Amer. Math. Soc. 355 (2003), 1521-1535
MSC (2000): Primary 11G18; Secondary 11F33, 14H55
Published electronically: November 20, 2002
MathSciNet review: 1946403
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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 $p$.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03204-X
PII: S 0002-9947(02)03204-X
Keywords: Weierstrass points, modular curves
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
Article copyright: © Copyright 2002 American Mathematical Society