Asymptotics for rank partition functions

2007/08/05 by Kathrin Bringmann, Bringmann, Kathrin
Mathematics · #05A17 #11P82 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:05A17 #msc:11P82

paper · pdf · doi:10.48550/arxiv.0708.0691

19 pages Transactions of the AMS, accepted for publication

arxiv created 2007/08/05 · openalex publication_date 2007/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The f(q) mock theta function conjecture and partition ranks

Related

• On the asymptotic behavior of unimodal rank generating functions
• Rank partition functions and truncated theta identities
• On the asymptotics of certain colored partitions
• Asymtotics for Moments of Higher Ranks
• A proof of some conjectures of Mao on partition rank inequalities