论文标题
Mathieu Moonshine和Siegel模块化形式
Mathieu Moonshine and Siegel Modular Forms
论文作者
论文摘要
第二个量化版本的Mathieu Moonshine导致了可能是siegel属模块化属的功能的产品公式，类似于Igusa cusp形式。这些函数的模块化并不明显地遵循。对于某些共轭类，但不是全部，它们匹配已知的模块化形式。在本文中，我们在标准模块化形式的产品方面表达了$ m_ {24} $的所有共轭类别的产品公式。这提供了他们的模块化的新证明。
A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner. For some conjugacy classes, but not all, they match known modular forms. In this paper, we express the product formulae for all conjugacy classes of $M_{24}$ in terms of products of standard modular forms. This provides a new proof of their modularity.
