Tetragonal modular quotients $X_0^*(N)$
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914114997059584 |
|---|---|
| author | Orlić, Petar |
| author_facet | Orlić, Petar |
| contents | Let $N$ be a positive integer. For every $d\mid N$ such that $(d,N/d)=1$ there exists an Atkin-Lehner involution $w_d$ of the modular curve $X_0(N)$. The curve $X_0^*(N)$ is a quotient curve of $X_0(N)$ by $B(N)$, the group of all involutions $w_d$. In this paper we determine all quotient curves $X_0^*(N)$ whose $\mathbb C$-gonality is equal to $4$. We also determine all curves $X_0^*(N)$ whose $\mathbb Q$-gonality is equal to $4$ with the exception of level $N=378$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tetragonal modular quotients $X_0^*(N)$ Orlić, Petar Number Theory Let $N$ be a positive integer. For every $d\mid N$ such that $(d,N/d)=1$ there exists an Atkin-Lehner involution $w_d$ of the modular curve $X_0(N)$. The curve $X_0^*(N)$ is a quotient curve of $X_0(N)$ by $B(N)$, the group of all involutions $w_d$. In this paper we determine all quotient curves $X_0^*(N)$ whose $\mathbb C$-gonality is equal to $4$. We also determine all curves $X_0^*(N)$ whose $\mathbb Q$-gonality is equal to $4$ with the exception of level $N=378$. |
| title | Tetragonal modular quotients $X_0^*(N)$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.22291 |