The Log-Behavior of $\sqrt[n]{p(n)}$ and $\sqrt[n]{p(n)/n}$

William Y. C. Chen, Ken Y. Zheng

Let $p(n)$ denote the partition function. Desalvo and Pak proved the log-concavity of $p(n)$ for $n>25$ and the inequality $\frac{p(n-1)}{p(n)}\left(1+\frac{1}{n}\right)>\frac{p(n)…