On the Fourier expansion of Bloch-Okounkov

Kathrin Bringmann; Antun Milas

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arXiv · 1412.6962

On the Fourier expansion of Bloch-Okounkov

Kathrin Bringmann·Antun Milas

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Abstract

In this paper, we study algebraic and analytic properties of Fourier coefficients, expressed as $q$-series, of the so-called Bloch-Okounkov $n$-point function. We prove several results about these series and explain how they relate to Rogers' false theta function. Then we obtain their full asymptotics, as $\tau \rightarrow 0$, and use this result to derive asymptotic properties of the coefficients in the $q$-expansion. At the end, we also introduce and discuss higher rank generalization of Bloch-Okounkov's functions.

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Kathrin Bringmann, Antun Milas. 2014-12-22. On the Fourier expansion of Bloch-Okounkov. https://arxiv.org/abs/1412.6962

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