Higher order log-concavity of the overpartition function and its consequences

2022/04/17 by Gargi Mukherjee, Mukherjee, Gargi, Helen W. J. Zhang +3 · 2 citations
Mathematics · #Analytic and geometric function theory #Analytic Number Theory Research #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2204.07961

Abstract

Let p(n) denote the overpartition function. In this paper, we study the asymptotic higher order log-concavity property of the overpatition 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 p(n-1)p(n+1)/p(n)² upto a certain order so that one can finally ends up with the phenomena of 2-log-concavity and higher order Turán property of p(n) by following a sort of unified approach.

Cited by

• Asymptotics of the shifted finite differences of the overpatition function and a problem of Wang--Xie--Zhang
• Asymptotics and inequalities for the distinct partition function

Related

• Log-concavity of the overpartition function
• Inequalities for the k-Regular Overpartitions
• Inequalities for the overpartition function arising from determinants
• Rademacher-type exact formula and higher order Turán inequalities for cubic overpartitions
• Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang