Twisted traces of modular functions on hyperbolic 3-space

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-07-21 DOI:10.1016/j.jnt.2025.06.010

S. Herrero , Ö. Imamoḡlu , A.-M. von Pippich , M. Schwagenscheidt

引用次数: 0

Abstract

We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic 3-space and show that they are essentially given by Fourier coefficients of the j-invariant. From this we deduce that the twisted traces of these harmonic modular functions are integers. Additionally, we compute the twisted traces of Eisenstein series on hyperbolic 3-space in terms of Dirichlet L-functions and divisor sums.

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双曲三维空间上模函数的扭曲迹

我们计算了双曲三维空间上调和模函数的CM值的扭曲轨迹的类似物，并证明了它们本质上是由j不变量的傅里叶系数给出的。由此我们推导出这些调和模函数的扭迹是整数。此外，我们用Dirichlet l -函数和除数和计算了双曲三维空间上爱森斯坦级数的扭曲迹。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.