Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Nie, Zhaohu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910658498
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