2007/12/05 by Yifan Yang, Yang, Yifan
Mathematics · #11F03 #11G16 #11G18 #14G05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.AG #math.NT #msc:11F03 #msc:11G16 #msc:11G18 #msc:14G05
paper · pdf · doi:10.48550/arxiv.0712.0629
43 pages
arxiv created 2007/12/05 · openalex publication_date 2007/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.