On an spt function for the $4$-th symmetrized crank function
Number Theory
2025-11-11 v1
Abstract
In this paper we find the smallest part function related to the -th symmetrized crank function, corresponding to the one obtained in Patkowski [11] for the -th symmetrized rank function. This provides us with a direct relationship with Garvan's second order smallest part function. We obtain some congruences for these functions, as well as asymptotics and inequalities. A finite -series which generates an function related to the second crank moment is also stated. This identity has an important relationship to the one obtained by Patkowski [12] related to the second rank moment.
Cite
@article{arxiv.2511.05857,
title = {On an spt function for the $4$-th symmetrized crank function},
author = {Alexander E. Patkowski},
journal= {arXiv preprint arXiv:2511.05857},
year = {2025}
}