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Complex multiplication of two eta-products

Volume 159 / 2020

Sungkon Chang Colloquium Mathematicum 159 (2020), 7-24 MSC: Primary 11F20; Secondary 11F30. DOI: 10.4064/cm7134-12-2018 Published online: 11 September 2019


The $q$-coefficients of a Hecke eigenform possess a multiplicative property, and in addition, if it has complex multiplication, the CM structure admits an efficient method of computing all coefficients. We use Euler’s pentagonal numbers theorem and Jacobi’s triangular numbers theorem to directly prove this CM phenomenon for two eta-products $\eta ^4(6\tau )$ and $\eta ^6(4\tau )$.


  • Sungkon ChangDepartment of Mathematics
    Georgia Southern University
    Armstrong Campus
    11935 Abercorn St.
    Savannah, GA 31419, U.S.A.

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