Siegel Product Expansion in M24 Moonshine

Martin Raum

We briefly revisit product expansions that were considered by Cheng, and Cheng and Duncan in the context of $M_{24}$-moonshine. To each conjugacy class $g$ of $M_{24}$, they attached a convergent product expansion $\Phi_g$ on the Siegel upper half plane of degree 2. It is expected that they are Siegel modular forms of some level which can be predicted in terms of properties of g alone.

http://scgp.stonybrook.edu/video_portal/video.php?id=2054

Simons- Program: Mock Modular Forms, Moonshine, and String Theory