Log-Concavity of the Partition Function

preprint2014arXivOpen access

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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Log-Concavity of the Partition Function

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