When is the Bloch–Okounkov q-bracket modular?

Jan Willem M. van Ittersum*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We obtain a condition describing when the quasimodular forms given by the Bloch–Okounkov theorem as q-brackets of certain functions on partitions are actually modular. This condition involves the kernel of an operator Δ. We describe an explicit basis for this kernel, which is very similar to the space of classical harmonic polynomials.

Original languageEnglish
Pages (from-to)1-14
JournalRamanujan Journal
Publication statusPublished - 1 Jan 2019


  • Harmonic polynomials
  • Modular forms
  • Partitions


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