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arXiv · 1909.12806

Asymptotic Distribution of the Partition Crank

Asimina Hamakiotes·Aaron Kriegman·Wei-Lun Tsai
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Abstract

The partition crank is a statistic on partitions introduced by Freeman Dyson to explain Ramanujan's congruences. In this paper, we prove that the crank is asymptotically equidistributed modulo Q, for any odd number Q. To prove this, we obtain effective bounds on the error term from Zapata Rolon's asymptotic estimate for the crank function. We then use those bounds to prove the surjectivity and strict log-subadditivity of the crank function.

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Asimina Hamakiotes, Aaron Kriegman, Wei-Lun Tsai. 2019-09-27. Asymptotic Distribution of the Partition Crank. https://arxiv.org/abs/1909.12806

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