Complex multiplication of two eta-products

Sungkon Chang

doi:10.4064/CM7134-12-2018

Complex multiplication of two eta-products

Sungkon Chang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 η⁴(6τ) and η⁶(4τ).

Original language	English
Pages (from-to)	7-24
Number of pages	18
Journal	Colloquium Mathematicum
Volume	159
Issue number	1
DOIs	https://doi.org/10.4064/CM7134-12-2018
State	Published - 2020

Keywords

Complex multiplication
Fourier coefficients of automorphic forms
eta-products

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10.4064/CM7134-12-2018

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abstract = "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{\textquoteright}s pentagonal numbers theorem and Jacobi{\textquoteright}s triangular numbers theorem to directly prove this CM phenomenon for two eta-products η4(6τ) and η6(4τ).",

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Complex multiplication of two eta-products

Abstract

Keywords

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