Abstract
We prove that the overpartition function \( \overline{p}(n)\) is log-concave for all \( n\ge 2 \). The proof is based on Sills-Rademacher-type series for \( \overline{p}(n)\) and inspired by DeSalvo and Pak’s proof for the partition function.
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References
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Acknowledgments
The author is grateful for useful advice and guidance from Professor Bringmann, Dr. Krauel, Dr. Li, Dr. Mertens, and Dr. Rolen.
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Engel, B. Log-concavity of the overpartition function. Ramanujan J 43, 229–241 (2017). https://doi.org/10.1007/s11139-015-9762-0
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DOI: https://doi.org/10.1007/s11139-015-9762-0