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

Fuente: arXiv
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Main Author: Lupoian, Elvira
Format: Preprint
Published: 2025
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author Lupoian, Elvira
author_facet Lupoian, Elvira
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_04084
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group
Lupoian, Elvira
Number Theory
11G16, 11G18
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.
title Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group
topic Number Theory
11G16, 11G18
url https://arxiv.org/abs/2502.04084