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arXiv · 2502.04084

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group

Elvira Lupoian
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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 $X_{1}( p )$, with prime level $p \ge 5$. 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 $X_{1}( p)$ 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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Elvira Lupoian. 2025-02-06. Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group. https://arxiv.org/abs/2502.04084

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