论文标题
Hecke的谐波功能和应用到较高属模块曲线的应用系统
Hecke System of Harmonic Maass Functions and Applications to Modular Curves of Higher Genera
论文作者
论文摘要
在可怕的月光中，属0属和可复制性概念密切相关。关于月光的最新发展，我们研究了一般自身形式的可复制性的较高属概括。具体而言，我们将重复的定义和Hecke操作员的定义扩展到谐波MAAS在较高属的模块化曲线上的功能，以获得数字的理论概括，这些理论概括是在巨大的月光中的重要结果。此外，我们显示了扩展概念在产生均匀证明的统一证明的实用性，以实现模块化水平模块化函数的傅立叶系数的众多算术特性，这仅是仅对于零属或小质量曲线曲线的特殊情况。
In Monstrous moonshine, genus 0 property and the notion of replicability are strongly connected. With regards to recent developments of moonshine, we investigate a higher genus generalization of replicability for a general automorphic form. Specifically, we extend the definitions of replicates and a Hecke operator to harmonic Maass functions on modular curves of higher genera to obtain number theoretic generalizations of important results in Monstrous moonshine. Furthermore, we show the utility of the extended notions in yielding uniform proofs for numerous arithmetic properties of Fourier coefficients of modular functions of arbitrary level, which have been proved only for special cases of curves of genus zero or small prime levels.
