On Dyson's crank conjecture and the uniform asymptotic behavior of\n certain inverse theta functions

2013/11/24 by Kathrin Bringmann, Bringmann, Kathrin, Jehanne Dousse +1
Mathematics · #05A17 #11F03 #11F30 #11F50 #11P55 #11P82 #14J60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1311.6089

openalex publication_date 2013/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a longstanding conjecture by Freeman Dyson concerning\nthe limiting shape of the crank generating function. We fit this function in a\nmore general family of inverse theta functions which play a key role in\nphysics.\n

Citations

• Dyson’s ranks and Maass forms

Related

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• Rank partition functions and truncated theta identities
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• Dyson's crank and unimodal compositions
• Asymptotics of crank generating functions and Ramanujan congruences