### 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.

Original language | English |
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Pages (from-to) | 439-453 |

Number of pages | 15 |

Journal | Letters in Mathematical Physics |

Volume | 103 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 2013 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Kaneko, M., Nagatomo, K., & Sakai, Y. (2013). Modular Forms and Second Order Ordinary Differential Equations: Applications to Vertex Operator Algebras.

*Letters in Mathematical Physics*,*103*(4), 439-453. https://doi.org/10.1007/s11005-012-0602-5