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arXiv · 1603.05608

On spt-crank type functions

Min-Joo Jang·Byungchan Kim
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Abstract

In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function $\operatorname{spt}_\omega(n)$, which is closely related to Ramanujan's third order mock theta function $\omega(q)$. Garvan and Jennings-Shaffer introduce a crank function which explains congruences for $\operatorname{spt}_\omega(n)$. In this note, we study asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We also study a sign pattern of the crank and congruences for $\operatorname{spt}_\omega(n)$.

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Min-Joo Jang, Byungchan Kim. 2016-03-17. On spt-crank type functions. https://arxiv.org/abs/1603.05608

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