Log-Concavity of the Partition Function
classification
🧮 math.CO
keywords
functionpartitionchenconjecturesestimatesextendhardy--ramanujanlehmer
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We prove that the partition function $p(n)$ is log-concave for all $n>25$. We then extend the results to resolve two related conjectures by Chen. The proofs are based on Lehmer's estimates on the remainders of the Hardy--Ramanujan and the Rademacher series for $p(n)$.
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