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Weierstrass points on certain modular groups
- Authors
- Im, Bo-Hae; Jeon, Daeyeol; Kim, Chang Heon
- Issue Date
- Mar-2016
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Weierstrass points; Modular curves
- Citation
- JOURNAL OF NUMBER THEORY, v.160, pp 586 - 602
- Pages
- 17
- Journal Title
- JOURNAL OF NUMBER THEORY
- Volume
- 160
- Start Page
- 586
- End Page
- 602
- ISSN
- 0022-314X
1096-1658
- Abstract
- 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.
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