Weierstrass points on certain modular groups

JOURNAL OF NUMBER THEORY

卷:160

Article

Im, Bo-Hae¹  Jeon, Daeyeol²  Kim, Chang Heon³ 

[1] Chung Ang Univ, Dept Math, Seoul 156756, South Korea

[2] Kongju Natl Univ, Dept Math Educ, Gongju Si 314701, Chungcheongnam, South Korea

[3] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

关键词: Weierstrass points;    Modular curves;   

DOI  :  10.1016/j.jnt.2015.09.018

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free