Quasimodular forms as solutions of Modular differential equations

Peter J. Grabner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study quasimodular forms of depth ≤ 4 and determine under which conditions they occur as solutions of modular differential equations. Furthermore, we study which modular differential equations have quasimodular solutions. We use these results to investigate extremal quasimodular forms as introduced by M. Kaneko and M. Koike further. Especially, we prove a conjecture stated by these authors concerning the divisors of the denominators occurring in their Fourier expansion.

Original languageEnglish
Pages (from-to)2233 - 2274
Number of pages42
JournalInternational Journal of Number Theory
Issue number10
Publication statusPublished - 1 Nov 2020


  • math.NT
  • 11F11 34A05
  • modular differential equations
  • Balanced quasimodular forms
  • quasimodular vectors
  • extremal quasimodular forms

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing


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