The modular automorphisms of quotient modular curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916736833421312 |
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| author | Bars, Francesc Dalal, Tarun |
| author_facet | Bars, Francesc Dalal, Tarun |
| contents | We obtain the modular automorphism group of any quotient modular curve of level $N$, with $4,9\nmid N$. In particular, we obtain some non-expected automorphisms of order 3 that appear for the quotient modular curves when the Atkin-Lehner involution $w_{25}$ belongs to the quotient modular group, such automorphisms are not necessarily defined over $\mathbb{Q}$. As a consequence of the results, we obtain the full automorphism group of the quotient modular curve $X_0^*(N^2)$, for sufficiently large $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The modular automorphisms of quotient modular curves Bars, Francesc Dalal, Tarun Number Theory Algebraic Geometry Group Theory We obtain the modular automorphism group of any quotient modular curve of level $N$, with $4,9\nmid N$. In particular, we obtain some non-expected automorphisms of order 3 that appear for the quotient modular curves when the Atkin-Lehner involution $w_{25}$ belongs to the quotient modular group, such automorphisms are not necessarily defined over $\mathbb{Q}$. As a consequence of the results, we obtain the full automorphism group of the quotient modular curve $X_0^*(N^2)$, for sufficiently large $N$. |
| title | The modular automorphisms of quotient modular curves |
| topic | Number Theory Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2505.08401 |