Log-Concavity of the Partition Function
Combinatorics
2014-07-07 v2
Abstract
We prove that the partition function is log-concave for all . 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 .
Keywords
Cite
@article{arxiv.1310.7982,
title = {Log-Concavity of the Partition Function},
author = {Stephen DeSalvo and Igor Pak},
journal= {arXiv preprint arXiv:1310.7982},
year = {2014}
}
Comments
8 pages, 1 figure, 20 references