The third order modular linear differential equations

Masanobu Kaneko, Kiyokazu Nagatomo, Yuichi Sakai

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume485
DOIs
Publication statusPublished - Sep 1 2017

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Linear differential equation
Generalized Hypergeometric Series
Modular Equations
Multiple Roots
Vertex Operator Algebras
Simple Module
Conformal Field Theory
Two Parameters
Classify
Exponent
Infinity
Differential equation
Character
Generalization

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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

In: Journal of Algebra, Vol. 485, 01.09.2017, p. 332-352.

Research output: Contribution to journalArticle

Kaneko, Masanobu ; Nagatomo, Kiyokazu ; Sakai, Yuichi. / The third order modular linear differential equations. In: Journal of Algebra. 2017 ; Vol. 485. pp. 332-352.
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