### 抄録

We propose a third order generalization of the Kaneko–Zagier modular differential equation, which has two parameters. We describe modular and quasimodular solutions of integral weight in the case where one of the exponents at infinity is a multiple root of the indicial equation. We also classify solutions of “character type”, which are the ones that are expected to relate to characters of simple modules of vertex operator algebras and one-point functions of two-dimensional conformal field theories. Several connections to generalized hypergeometric series are also discussed.

元の言語 | 英語 |
---|---|

ページ（範囲） | 332-352 |

ページ数 | 21 |

ジャーナル | Journal of Algebra |

巻 | 485 |

DOI | |

出版物ステータス | 出版済み - 9 1 2017 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### これを引用

*Journal of Algebra*,

*485*, 332-352. https://doi.org/10.1016/j.jalgebra.2017.05.007

**The third order modular linear differential equations.** / Kaneko, Masanobu; Nagatomo, Kiyokazu; Sakai, Yuichi.

研究成果: ジャーナルへの寄稿 › 記事

*Journal of Algebra*, 巻. 485, pp. 332-352. https://doi.org/10.1016/j.jalgebra.2017.05.007

}

TY - JOUR

T1 - The third order modular linear differential equations

AU - Kaneko, Masanobu

AU - Nagatomo, Kiyokazu

AU - Sakai, Yuichi

PY - 2017/9/1

Y1 - 2017/9/1

N2 - We propose a third order generalization of the Kaneko–Zagier modular differential equation, which has two parameters. We describe modular and quasimodular solutions of integral weight in the case where one of the exponents at infinity is a multiple root of the indicial equation. We also classify solutions of “character type”, which are the ones that are expected to relate to characters of simple modules of vertex operator algebras and one-point functions of two-dimensional conformal field theories. Several connections to generalized hypergeometric series are also discussed.

AB - We propose a third order generalization of the Kaneko–Zagier modular differential equation, which has two parameters. We describe modular and quasimodular solutions of integral weight in the case where one of the exponents at infinity is a multiple root of the indicial equation. We also classify solutions of “character type”, which are the ones that are expected to relate to characters of simple modules of vertex operator algebras and one-point functions of two-dimensional conformal field theories. Several connections to generalized hypergeometric series are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=85020008441&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020008441&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.05.007

DO - 10.1016/j.jalgebra.2017.05.007

M3 - Article

VL - 485

SP - 332

EP - 352

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -