標題: | Modular units and cuspidal divisor class groups of X-1(N) |
作者: | Yang, Yifan 應用數學系 Department of Applied Mathematics |
關鍵字: | Modular units;Cuspidal divisor class groups of modular curves |
公開日期: | 15-七月-2009 |
摘要: | In this article, we consider the group F-1(infinity)(N) of modular units on X-1(N) that have divisors supported on the cusps lying over infinity of X-0(N), called the infinity-cusps. For each positive integer N, we will give an explicit basis for the group F-1(infinity)(N). This enables us to compute the group structure of the rational torsion subgroup l(1)(infinity)(N) of the Jacobian J(1)(N) of X-1(N) generated by the differences of the infinity-cusps. In addition, based on our numerical computation, we make a conjecture on the structure of the p-primary part of l(1)(infinity)(p(n)) for a regular prime p. (C) 2009 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.jalgebra.2009.04.012 http://hdl.handle.net/11536/149788 |
ISSN: | 0021-8693 |
DOI: | 10.1016/j.jalgebra.2009.04.012 |
期刊: | JOURNAL OF ALGEBRA |
Volume: | 322 |
起始頁: | 514 |
結束頁: | 553 |
顯示於類別: | 期刊論文 |