Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912222143315968 |
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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 |