M24-twisted Product Expansions are Siegel Modular Forms
Abstract
Cheng constructed product expansions from twists of elliptic genera of symmetric powers of K3 surfaces that are related to M24 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.
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