Asymptotics for rank partition functions
Kathrin Bringmann
TL;DR
This paper derives asymptotic formulas for a broad class of rank generating functions and applies these results to prove a conjecture regarding inequalities between different ranks.
Contribution
It introduces new asymptotic formulas for rank generating functions and resolves a conjecture by Andrews and Lewis.
Findings
Derived asymptotic formulas for rank generating functions
Proved a conjecture on inequalities between ranks
Enhanced understanding of rank distribution asymptotics
Abstract
In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research