2021
DOI: 10.1007/jhep03(2021)050
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Mathieu moonshine and Siegel Modular Forms

Abstract: A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner. For some conjugacy classes, but not all, they match known modular forms. In this paper, we express the product formulae for all conjugacy classes of M24 in terms of products of standard modular forms. This provides a new proof of their modularity.

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Cited by 3 publications
(4 citation statements)
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“…The above tables were constructed using Sen's formula (2.4), and we verified that they match with the Cléry-Gritsenko formula [27,42,43]. Implementation of Cléry-Gritsenko formula is in fact easier in Mathematica and computation time is shorter, especially for the higher values of N .…”
Section: Comment About the Implementationmentioning
confidence: 63%
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“…The above tables were constructed using Sen's formula (2.4), and we verified that they match with the Cléry-Gritsenko formula [27,42,43]. Implementation of Cléry-Gritsenko formula is in fact easier in Mathematica and computation time is shorter, especially for the higher values of N .…”
Section: Comment About the Implementationmentioning
confidence: 63%
“…Some work in this direction has already been done in [23]. We note that, for twining partition functions (no twisting) these proofs have been recently completed [27,43]. We hope to return to some of the above problems in our future work.…”
Section: ×mentioning
confidence: 94%
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“…However, it follows from a result in ref. [18] that it is a Siegel modular form of a level N subgroup of Sp(4, Z).…”
Section: Embeddingmentioning
confidence: 99%