When is the Bloch–Okounkov q-bracket modular?

Jan Willem M. van Ittersum

doi:10.1007/s11139-019-00144-1

When is the Bloch–Okounkov q-bracket modular?

Jan Willem M. van Ittersum^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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 language	English
Pages (from-to)	1-14
Journal	Ramanujan Journal
DOIs	https://doi.org/10.1007/s11139-019-00144-1
Publication status	Published - 1 Jan 2019

Keywords

Harmonic polynomials
Modular forms
Partitions

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10.1007/s11139-019-00144-1

Ittersum2019_Article_WhenIsTheBlochOkounkovQ-brackeFinal published version, 295 KB

Cite this

@article{5e29a2cde4a04f0db60554cc406d92bb,

title = "When is the Bloch–Okounkov q-bracket modular?",

abstract = "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.",

keywords = "Harmonic polynomials, Modular forms, Partitions",

author = "{van Ittersum}, {Jan Willem M.}",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/s11139-019-00144-1",

language = "English",

pages = "1--14",

journal = "Ramanujan Journal",