# Min-Joo Jang

Affiliation: University of Cologne

Email: min-joo.jang@uni-koeln.de

Title Of Talk: On spt-crank type functions

Abstract: In a recent paper, Andrews, Dixit, and Yee introduce a new spt-type function $\spt_\omega(n)$, which closely related with Ramanujan's third order mock theta function $\omega(q)$. Garvan and Jennings-Shaffer introduce a crank function which explain congruences for $\spt_\omega(n)$. In this talk, 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 $\spt_\omega(n)$. This is joint work with Byungchan Kim.