Proceedings of the Japan Academy, Series A, Mathematical Sciences

Trigonal quotients of modular curves $X_{0}(N)$

Yuji Hasegawa and Mahoro Shimura

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Abstract

Let $W(N)$ be the group of Atkin-Lehner involutions on the modular curve $X_0(N)$. The purpose of this article is to give complementary result to [7, 8, 9]; namely, we determine trigonal curves of the form $X_0(N)/W'$, where $W'$ is a subgroup of $W(N)$ such that $2< |W'| < |W(N)|$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 82, Number 2 (2006), 15-17.

Dates
First available in Project Euclid: 2 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1141279058

Digital Object Identifier
doi:10.3792/pjaa.82.15

Mathematical Reviews number (MathSciNet)
MR2209765

Zentralblatt MATH identifier
1115.11031

Subjects
Primary: 11F03: Modular and automorphic functions 11F12: Automorphic forms, one variable 11F11: Holomorphic modular forms of integral weight
Secondary: 11G30: Curves of arbitrary genus or genus = 1 over global fields [See also 14H25] 14H25: Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx] 14H50: Plane and space curves 11G05: Elliptic curves over global fields [See also 14H52]

Keywords
Modular curve modular form gonality plane curve

Citation

Hasegawa, Yuji; Shimura, Mahoro. Trigonal quotients of modular curves $X_{0}(N)$. Proc. Japan Acad. Ser. A Math. Sci. 82 (2006), no. 2, 15--17. doi:10.3792/pjaa.82.15. https://projecteuclid.org/euclid.pja/1141279058


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