Asymtotics for Moments of Higher Ranks

TL;DR

This paper extends asymptotic analysis methods to higher rank partition statistics, generalizing previous work on rank and crank moments to include the T-rank for odd T, such as T=3.

Contribution

It introduces a framework for deriving asymptotics for moments of higher rank partition statistics, expanding the scope of prior results.

Findings

Derived asymptotic expressions for higher rank moments

Extended methods to T-rank for odd T values

Generalized previous asymptotic formulas

Abstract

Bringmann, Mahlburg, and Rhoades have found asymptotic expressions for all moments of the partition statistics rank and crank. In this work we extend their methods to higher ranks. The $T$-rank, introduced by Garvan, for odd integers T=3 is a natural generalization of the rank (T=3) and crank (T=1).