Modular units and cuspidal divisor class groups of X1 (N)
Journal
Journal of Algebra
Journal Volume
322
Journal Issue
2
Pages
514-553
Date Issued
2009
Author(s)
Abstract
In this article, we consider the group F1∞ (N) of modular units on X1 (N) that have divisors supported on the cusps lying over ∞ of X0 (N), called the ∞-cusps. For each positive integer N, we will give an explicit basis for the group F1∞ (N). This enables us to compute the group structure of the rational torsion subgroup C1∞ (N) of the Jacobian J1 (N) of X1 (N) generated by the differences of the ∞-cusps. In addition, based on our numerical computation, we make a conjecture on the structure of the p-primary part of C1∞ (pn) for a regular prime p. © 2009 Elsevier Inc. All rights reserved.
Type
journal article