When is the Bloch-Okounkov q-bracket modular?

van Ittersum, Jan-Willem M.

doi:10.1007/s11139-019-00144-1

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When is the Bloch-Okounkov q-bracket modular?

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van Ittersum, Jan-Willem M.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s11139-019-00144-1
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arXiv:1810.06987.pdf
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vanIttersume_When is the Bloch-Okounkov q-bracket modular_2020.pdf
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van Ittersum, J.-W.-M. (2020). When is the Bloch-Okounkov q-bracket modular? Ramanujan Journal, 52(3), 669-682. doi:10.1007/s11139-019-00144-1.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9EF5-4

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 {\Delta}.
We describe an explicit basis for this kernel, which is very similar to the space of classical harmonic polynomials.