Mathieu moonshine and Borcherds products
The twined elliptic genera of K3 a surface associated with the conjugacy classes of the Mathieu group M24 are known to be weak Jacobi forms of weight 0 . In 2010, Cheng constructed formal infinite products from the twined elliptic genera and conjectured that they define Siegel modular forms of degre...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
14 February 2025
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| In: |
Communications in number theory and physics
Year: 2025, Volume: 19, Issue: 1, Pages: 135-168 |
| ISSN: | 1931-4531 |
| DOI: | 10.4310/CNTP.250215003845 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.4310/CNTP.250215003845 Verlag, lizenzpflichtig, Volltext: https://link.intlpress.com/JDetail/1890441252077895681 
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| Author Notes: | Haowu Wang and Brandon Williams |
| Summary: | The twined elliptic genera of K3 a surface associated with the conjugacy classes of the Mathieu group M24 are known to be weak Jacobi forms of weight 0 . In 2010, Cheng constructed formal infinite products from the twined elliptic genera and conjectured that they define Siegel modular forms of degree two. In this paper we prove that for each conjugacy class of level N9 the associated product is a meromorphic Borcherds product on the lattice U(Ng) ⊗ U ⊗ A1 in a strict sense. We also compute the divisors of these products and determine for which conjugacy classes the product can be realized as an additive (generalized Saito-Kurokawa) lift. |
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| Item Description: | Gesehen am 08.12.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1931-4531 |
| DOI: | 10.4310/CNTP.250215003845 |