Mathieu Moonshine and Siegel Modular Forms
High Energy Physics - Theory
2021-06-07 v3 Group Theory
Number Theory
Abstract
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 in terms of products of standard modular forms. This provides a new proof of their modularity.
Cite
@article{arxiv.2011.07922,
title = {Mathieu Moonshine and Siegel Modular Forms},
author = {Suresh Govindarajan and Sutapa Samanta},
journal= {arXiv preprint arXiv:2011.07922},
year = {2021}
}
Comments
35 pages; v2: Main proposition has been corrected leading to a single formula; referencing has been improved v3: Improved presentation (final version)