Log-concavity of the partition function

By Stephen Desalvo, Igor Pak. 2013

159 citations recorded by the source corpus.

We prove that the partition function $$p(n)$$p(n) is log-concave for all $$n>25$$n>25. We then extend the results to resolve two related conjectures by Chen and one by Sun. The proofs are based on Lehmer’s estimates on the remainders of the Hardy–Ramanujan and the Rademacher series for $$p(n)$$p(n).

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/ffff82b5f0f049f4c16cf9f6a4dde8e1cddf4389

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In Algebra and Number Theory

1. Dennis X. Q. Jia
2. Larry X. W. Wang
3. William Y. C. Chen

In Discrete Mathematics and Combinatorics

1. Dennis X. Q. Jia
2. Larry X. W. Wang
3. William Y. C. Chen

Citations in the corpus

• Higher order Turán inequalities for the partition function (2017, methodology): “We shall make use of the fact that un < 1 for n ≥ 26, as proved by DeSalvo and Pak [13].”