至多有有限多个为 S-单位的奇异模
数论
2023-09-07 v3 代数几何
动力系统
摘要
我们证明，对每一个有限素数集合 S，至多有有限多个为 S-单位的奇异模。关键的新要素在于，对每个素数 p，奇异模在 p 进意义下是分散的。我们对韦伯模函数、lambda 不变量以及与怪兽群元素相关的 McKay-Thompson 级数证明了类似结果。最后，我们还得到，一个模函数若在二次虚数处取到无穷多个代数单位，则必为弱模单位。
引用
@article{arxiv.2102.05041,
title = {There are at most finitely many singular moduli that are S-units},
author = {Sebastián Herrero and Ricardo Menares and Juan Rivera-Letelier},
journal= {arXiv preprint arXiv:2102.05041},
year = {2023}
}
备注
Improved version of Theorem A. Corrected Lemma 2.8(ii), which was false as stated in the previous version (this does not affect the main results). Accepted for publication in Compositio Mathematica