Quasimodularity of the $k$th Residual Cranks

Thomas Morrill; Aleksander Simonič

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arXiv · 2005.01919

Quasimodularity of the $k$th Residual Cranks

Thomas Morrill·Aleksander Simonič

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Abstract

We establish quasimodularity for a family of residual crank generating functions defined on overpartitions. We also show that the second moments of these $k$th residual cranks admit a combinatoric interpretation as weighted overpartition counts.

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Thomas Morrill, Aleksander Simonič. 2020-05-05. Quasimodularity of the $k$th Residual Cranks. https://arxiv.org/abs/2005.01919

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