Weierstrass points on certain modular groups

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We investigate Weierstrass points of the modular curve X-Delta(N) of genus >= 2 when Delta is a proper subgroup of (Z/NZ)*. Let N = p(2)M where p is a prime number and M is a positive integer. Modifying Atkin's method in the case +/-(1 + pM) is an element of A, we find conditions for the cusp 0 to be a Weierstrass point on the modular curve X-Delta(p(2)M). Moreover, applying Schoneberg's theorem we show that except for finitely many N, the fixed points of the Fricke involutions W-N are Weierstrass points on X-Delta(N). (C) 2015 Elsevier Inc. All rights reserved
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2016-03
Language
English
Article Type
Article
Citation

JOURNAL OF NUMBER THEORY, v.160, pp.586 - 602

ISSN
0022-314X
DOI
10.1016/j.jnt.2015.09.018
URI
http://hdl.handle.net/10203/212928
Appears in Collection
MA-Journal Papers(저널논문)
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