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Modular Forms and Second Order Ordinary Differential Equations: Applications to Vertex Operator Algebras |
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| Authors: | Masanobu Kaneko Kiyokazu Nagatomo Yuichi Sakai |
| Affiliation: | 1. Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan 2. Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan 3. Yokomizo 3012-2, Ooki-machi, Mizuma-gun, Fukuoka, 830-0405, Japan |
| Abstract: | We study the relation between the Kaneko–Zagier equation and the Mathur–Mukhi–Sen classification, and extend it to the case of solutions with logarithmic terms, which correspond to pseudo-characters of non-rational vertex operator algebras. As an application, we prove a non-existence theorem of rational vertex operator algebras. |
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