Communications in Number Theory and Physics

Volume 7 (2013)

Number 3

$M_{24}$-twisted product expansions are Siegel modular forms

Pages: 469 – 495



Martin Raum (Max Planck Institut für Mathematik, Bonn, Germany)


Cheng constructed product expansions from twists of elliptic genera of symmetric powers of $K3$ surfaces that are related to $M_{24}$ moonshine. We study which of them are Siegel modular forms. If the predicted level is non-composite, they are modular, and their powers can be represented as products of rescaled Borcherds products.

Full Text (PDF format)