M24-twisted Product Expansions are Siegel Modular Forms
classification
🧮 math.NT
keywords
modularexpansionsformspowersproductproductssiegelborcherds
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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.
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