Rademacher符号的双曲类比
数论
2025-04-01 v4
摘要
Dedekind最著名的结果之一是的变换律。半个世纪后，Rademacher修正了Dedekind的结果，并引入了一个-共轭类不变量（整值）函数，称为Rademacher符号。受Ghys关于模纽结工作的启发，Duke-Imamo\={g}lu-T\'{o}th (2017)构造了该符号的双曲类比。在本文中，我们研究他们的Rademacher符号双曲类比，并通过与经典Rademacher符号比较给出其两类显式公式。与此相关，我们对比展示了抛物、椭圆与双曲Eisenstein级数的Kronecker极限型公式。这些极限给出了权为2的调和、极调和与局部调和Maass形式。
引用
@article{arxiv.2003.12354,
title = {A Hyperbolic Analogue of the Rademacher Symbol},
author = {Toshiki Matsusaka},
journal= {arXiv preprint arXiv:2003.12354},
year = {2025}
}
备注
38 pages. This article is published in Mathematische Annalen. It differs from v3 with the addition of a new Appendix B. Furthermore, while Appendix C has been removed in the published version, it remains unchanged in this preprint