Modular unit and cuspidal divisor class groups of X_1(N)
| dc.creator | Yang, Yifan | |
| dc.date | 2007-12-05 | |
| dc.date.accessioned | 2026-07-07T08:47:23Z | |
| dc.date.available | 2026-07-07T08:47:23Z | |
| dc.description | In this article, we consider the group $F_1^\infty(N)$ of modular units on $X_1(N)$ that have divisors supported on the cusps lying over $\infty$ of $X_0(N)$, called the $\infty$-cusps. For each positive integer $N$, we will give an explicit basis for the group $F_1^\infty(N)$. This enables us to compute the group structure of the rational torsion subgroup $C_1^\infty(N)$ of the Jacobian $J_1(N)$ of $X_1(N)$ generated by the differences of the $\infty$-cusps. In addition, based on our numerical computation, we make a conjecture on the structure of the $p$-primary part of $C_1^\infty(p^n)$ for a regular prime $p$. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/0712.0629 | |
| dc.identifier | http://arxiv.org/abs/0712.0629 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143580 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G16; 11G18; 11F03; 14G05 | |
| dc.title | Modular unit and cuspidal divisor class groups of X_1(N) | |
| dc.type | text |