The third order modular linear differential equations

Masanobu Kaneko, Kiyokazu Nagatomo, Yuichi Sakai

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)332-352
    Number of pages21
    JournalJournal of Algebra
    Publication statusPublished - Sept 1 2017

    All Science Journal Classification (ASJC) codes

    • Algebra and Number Theory


    Dive into the research topics of 'The third order modular linear differential equations'. Together they form a unique fingerprint.

    Cite this