Log-concavity of the overpartition function

TL;DR

This paper proves that the overpartition function exhibits log-concavity for all integers greater than one, using series representations and methods inspired by similar proofs for the partition function.

Contribution

It establishes the log-concavity of the overpartition function for all n>1, extending known properties of partition functions to overpartitions.

Findings

Overpartition function is log-concave for all n>1

Proof utilizes Rademacher type series for overpartitions

Inspired by Desalvo and Pak's approach for partition functions

Abstract

We prove that the overpartition function is log-concave for all n>1. The proof is based on Sills Rademacher type series for the overpartition function and inspired by Desalvo and Pak's proof for the partition function.