Title: Modular units and cuspidal divisor class groups of X(1)(N)
Authors: Yang, Yifan
Department of Applied Mathematics
Issue Date: 15-Jul-2009
Abstract: 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
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.04.012
Volume: 322
Issue: 2
Begin Page: 514
End Page: 553
Appears in Collections:Articles