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Higher order log-concavity of the overpartition function and its consequences
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Journal Article
Higher order log-concavity of the overpartition function and its consequences
2023
Overview
Let
${\\overline{p}}(n)$ denote the overpartition function. In this paper, we study the asymptotic higher-order log-concavity property of the overpartition function in a similar framework done by Hou and Zhang for the partition function. This will enable us to move on further in order to prove log-concavity of overpartitions, explicitly by studying the asymptotic expansion of the quotient
${\\overline{p}}(n-1){\\overline{p}}(n+1)/{\\overline{p}}(n)^2$ up to a certain order. This enables us to additionally prove 2-log-concavity and higher Turán inequalities with a unified approach.
Publisher
Cambridge University Press
Subject
