On spt-crank type functions
Number Theory
2016-10-20 v2
Abstract
In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function , which is closely related to Ramanujan's third order mock theta function . Garvan and Jennings-Shaffer introduce a crank function which explains congruences for . 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 .
Cite
@article{arxiv.1603.05608,
title = {On spt-crank type functions},
author = {Min-Joo Jang and Byungchan Kim},
journal= {arXiv preprint arXiv:1603.05608},
year = {2016}
}