Modular Units on X₁( p) and Quotients of the Cuspidal Group

2025/02/06 by Elvira Lupoian, Lupoian, Elvira
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.04084

Abstract

Modular units are functions on modular curves whose divisors are supported on the cusps. They form a free abelian group of rank at most one less than the number of cusps. In this paper we study the group of modular units on X₁( p ), with prime level p ≥ 5. We give an explicit basis for this group and study certain rational subgroups of it. We use the basis to numerically investigate the structure of the cuspidal group of X₁( p) and its rational subgroup. In the later stages of this paper we use our basis to determine a specific large quotient of the cuspidal group.

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