与实二次域相关的模形式：作为循环积分的迹
Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals
- University of Cologne（科隆大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文针对局部调和Maaß形式实例少、缺乏统一理论的问题，证明Zagier的$f_{k,D}$与Mono的$g_{k+1,D}$函数作为循环积分迹的表示不唯一，丰富了相关理论研究。
中文摘要 AI 辅助
十年前，Bringmann、Kane和Kohnen在负权情形下首次建立了局部调和Maaß形式，Hövel则独立在权0情形下完成了相关工作。此后这些形式在与新形式的扭曲中心L值相关领域有重要应用，但目前已知的此类形式实例极少，尤其缺乏统一理论。本文针对该方向，证明Zagier的$f_{k,D}$函数与Mono的$g_{k+1,D}$函数作为循环积分迹的表示并非唯一。
英文摘要
A decade ago, locally harmonic Maaß forms were first established by Bringmann, Kane, and Kohnen in negative weights and independently by Hövel in weight $0$. Since then, they have seen important applications related to twisted central $L$-values of newforms. However, there are just a few examples of these forms known so far, and in particular there is no unifying theory behind these examples. Towards this direction, we show that the representations of Zagier's $f_{k,D}$ and Mono's $g_{k+1,D}$ functions as traces of cycle integrals are not unique.
