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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.12352 |
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Table of Contents:
- For $N>1$, we constructed a canonical connected fundamental domain for $Γ_0(N)$ in [Nie, Parent], utilizing an interesting function $W: {\mathbb Z}/N\to {\mathbb N}$. In this paper, we further study the function $W$, prove some identities, and use it to match the cusps, with widths, produced by our connected fundamental domain with the known cusp classes of $Γ_0(N)$. Furthermore, we list the boundary arcs and the gluing patterns of our connected fundamental domain, a key step in understanding the modular curve $X_0(N)$ by this approach.