PreprintCC BY 4.0arXiv
Cuspidal Class Number Formulae for Intermediate Modular Curves of Prime Level
Abstract
Let X be a modular curve lying between X0(p) and X1(p), where p ≥ 13 is prime. The cuspidal group of X is the subgroup of its Jacobian generated by the equivalence classes of differences of cusps. In this paper, we give explicit formulae for the order of the cuspidal group, and two subgroups of it defined over the rationals.
Related
- Residual finiteness and cuspidal cohomology of Picard modular surfaces
- Prym--Tyurin varieties coming from intermediate coverings of curves
- Arithmetic Siegel--Weil formula on the product of modular curves
- Rational Points on Drinfeld Modular Curves of Prime Level
- Modular and Shimura curves X0D(N) embedded in ℙ1 × ℙ1
BibTeX
@misc{lupoian2026cuspidal,
title = {{Cuspidal Class Number Formulae for Intermediate Modular Curves of Prime Level}},
author = {Elvira Lupoian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23690},
eprint = {2610.23690},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23690},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cuspidal Class Number Formulae for Intermediate Modular Curves of Prime Level
AU - Elvira Lupoian
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23690
UR - https://arxiv.org/abs/2610.23690
AB - Let X be a modular curve lying between X_0(p) and X_1(p), where p ≥ 13 is prime. The cuspidal group of X is the subgroup of its Jacobian generated by the equivalence classes of differences of cusps. In this paper, we give explicit formulae for the order of the cuspidal group, and two subgroups of it defined over the rationals.
ER -