Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group
Number Theory
2025-02-07 v1
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 , with prime level . 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 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.
Cite
@article{arxiv.2502.04084,
title = {Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group},
author = {Elvira Lupoian},
journal= {arXiv preprint arXiv:2502.04084},
year = {2025}
}